This is a multi-part message in MIME format. ---------------0604110849653 Content-Type: text/plain; name="06-113.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="06-113.keywords" relativistic quantum field theory, Unruh effect, thermal field, Fermi golden rule, quantum resonances, spectral deformation, return to equilibrium, Klein-Gordon ---------------0604110849653 Content-Type: application/postscript; name="unruh_m.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="unruh_m.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.94b Copyright 2004 Radical Eye Software %%Title: unruh_m.dvi %%Pages: 20 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: SFRM1728 SFRM1200 CMSY8 SFBX0900 SFRM0900 CMMI9 CMR9 %%+ CMR6 CMMI6 SFBX1440 SFRM1000 CMMI10 SFTI1000 CMR10 MSBM7 CMMI7 CMR7 %%+ CMR5 CMSY6 SFRM0800 CMSY7 CMSY10 SFBX1000 SFBX1200 MSBM10 CMEX10 %%+ CMMI5 MSAM10 CMSY5 LASY10 TeX-cmex7 CMMI12 CMMI8 CMR12 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o unruh_m.ps unruh_m.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2006.04.11:1426 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: cm-super-t1.enc 0 0 % This file is generated from `T1uni.map' and `glyphlist.txt', `gl-other.txt' % % LIGKERN hyphen hyphen =: endash ; 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cleartomark %%EndFont %%BeginFont: TeX-cmex7 %!PS-AdobeFont-1.0: TeX-cmex7 001.001 % Filtered by type1fix.pl 0.05 %%EndComments 13 dict dup begin /FontInfo 16 dict dup begin /Copyright (see\040copyright\040of\040original\040TeX\040font) def /FamilyName (TeX\040cmex7) def /FullName (TeX\040cmex7\040Regular) def /ItalicAngle 0 def /Notice (converted\040after\040April\0402001) def /UnderlinePosition -100 def /UnderlineThickness 50 def /Weight (Regular) def /isFixedPitch false def /version (001.001) def end readonly def /FontName /TeX-cmex7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 101 /e put readonly def /FontBBox {-14 -2954 1627 771} readonly def /UniqueID 4314415 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: LASY10 %!PS-AdobeFont-1.1: LASY10 1.001 %%CreationDate: 1992 Oct 23 20:19:17 %%RevisionDate: 2001 Jun 05 20:19:17 % Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.001) readonly def /Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def /FullName (LASY10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /LASY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 50 /a50 put readonly def /FontBBox{-19 -192 944 683}readonly def /UniqueID 5011949 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY5 %!PS-AdobeFont-1.1: CMSY5 1.0 %%CreationDate: 1991 Aug 15 07:21:16 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 48 /prime put dup 63 /perpendicular put readonly def /FontBBox{21 -944 1448 791}readonly def /UniqueID 5000815 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSAM10 %!PS-AdobeFont-1.1: MSAM10 2.1 %%CreationDate: 1993 Sep 17 09:05:00 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSAM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSAM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /square put dup 4 /squaresolid put dup 22 /harpoonupright put readonly def /FontBBox{8 -463 1331 1003}readonly def /UniqueID 5031981 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI5 %!PS-AdobeFont-1.1: CMMI5 1.100 %%CreationDate: 1996 Aug 02 08:21:10 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 21 /lambda put dup 25 /pi put dup 28 /tau put dup 33 /omega put dup 69 /E put dup 97 /a put dup 100 /d put dup 110 /n put readonly def /FontBBox{37 -250 1349 750}readonly def /UniqueID 5087380 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA06DA87FC7163A5A2A756A598FAB07633 89DE8BB201D5DB4627484A80A431B6AFDBBBF23D4157D4AFE17E6B1C853DD417 25F84CD55402AB88AB7EEFDEDBF2C2C731BD25567C53B474CCF739188A930039 098A197F9C4BE7594D79442B2C8A67447DE44698321145D7689B91EF235EA80E B600AA8E238064F154284096C4C2554EFE8DDF13AFF8D3CE30E0999375C0FEE6 F992DEA5FC3897E2CC8B7A90238E61E41622DE80F438DD994C73275CC52249D9 F6686F87F394FB7BB668138B210BEC9E46415A1B58C990B81E7D7DD301143517 4C2A259D2A0A1E200F8101469C10D7D537B0D4D39296A9AB3F132DA9A3B459B0 F850E2B3A03BDCB35AEF82285D19C38F474FB414F8EC971B994D1C7DD753B271 2B71549DF497C665DF0F266988209D9EB616E4D9BA229FF984E7A886DB01FD21 48ED2E4859FD6416C2CE52537464EA884C8C9C2D1083E2B83BE4B766474C23B6 6E8EC5003200AB10514BB44D14CA700416AB6B2683E80862E7D5B49A05526A32 554BB23AB8B0824BBA198E3825CE82380CC0FECF46651E3E5D77F09465E73164 20342822F29572BC7F73F2C3BF95ED3BB6FDEADC20C6AC866C4F2C679594D7E8 8D944704A3C5D771DC39503BECAB89F34D8CDB8FDB91AFE21F3F0260D05E90C5 73E2C13DFA022C4522E5918EE25038A0498FBB530DA33B0AE238B1C6ED03FC04 2BFED8236E07820C5BAB411EAE1B31D93A2FA7C374B1725FEC359ABCB88E2C89 214529A263D795AACB0B95A3AB2F4E08EF350C282CE521716DBB06E5B8291B3F 5D4ACA230FA192F64BC902A4C8842C0F916F92FBD002ADD408BF0401D0284FBB F05D4C6DB631420747CC902C5E1617E6573612FB26C8378DF41FFB5048D3CF06 4893DBA48EF4B043D760F60C75712169D16C83EE020C45369E443E853E1809DD 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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /parenleftbig put dup 1 /parenrightbig put dup 2 /bracketleftbig put dup 3 /bracketrightbig put dup 8 /braceleftbig put dup 9 /bracerightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 26 /braceleftbigg put dup 34 /bracketleftBigg put dup 35 /bracketrightBigg put dup 50 /bracketlefttp put dup 51 /bracketrighttp put dup 52 /bracketleftbt put dup 53 /bracketrightbt put dup 54 /bracketleftex put dup 55 /bracketrightex put dup 80 /summationtext put dup 82 /integraltext put dup 88 /summationdisplay put dup 90 /integraldisplay put dup 98 /hatwide put dup 99 /hatwider put dup 101 /tildewide put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put dup 112 /radicalbig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 2 /multiply put dup 6 /plusminus put dup 7 /minusplus put dup 8 /circleplus put dup 10 /circlemultiply put dup 14 /openbullet put dup 17 /equivalence put dup 20 /lessequal put dup 21 /greaterequal put dup 26 /propersubset put dup 33 /arrowright put dup 35 /arrowdown put dup 40 /arrowdblleft put dup 41 /arrowdblright put dup 47 /proportional put dup 49 /infinity put dup 50 /element put dup 51 /owner put dup 54 /negationslash put dup 55 /mapsto put dup 56 /universal put dup 65 /A put dup 66 /B put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 76 /L put dup 83 /S put dup 92 /intersection put dup 102 /braceleft put dup 103 /braceright put dup 104 /angbracketleft put dup 105 /angbracketright put dup 106 /bar put dup 107 /bardbl put dup 112 /radical put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 1 /periodcentered put dup 3 /asteriskmath put dup 6 /plusminus put dup 20 /lessequal put dup 21 /greaterequal put dup 33 /arrowright put dup 48 /prime put dup 49 /infinity put dup 50 /element put dup 63 /perpendicular put dup 70 /F put dup 72 /H put dup 106 /bar put dup 121 /dagger put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 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cleartomark %%EndFont %%BeginFont: CMSY6 %!PS-AdobeFont-1.1: CMSY6 1.0 %%CreationDate: 1991 Aug 15 07:21:34 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 3 /asteriskmath put dup 121 /dagger put readonly def /FontBBox{-4 -948 1329 786}readonly def /UniqueID 5000816 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 66 /B put dup 68 /D put dup 70 /F put readonly def /FontBBox{-341 -250 1304 965}readonly def /UniqueID 5000788 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 10 /Omega put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 59 /semicolon put dup 61 /equal put dup 66 /B put dup 68 /D put dup 70 /F put dup 73 /I put dup 76 /L put dup 82 /R put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 99 /c put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 114 /r put dup 115 /s put dup 118 /v put dup 120 /x put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 12 /beta put dup 15 /epsilon1 put dup 17 /eta put dup 18 /theta put dup 21 /lambda put dup 25 /pi put dup 27 /sigma put dup 28 /tau put dup 33 /omega put dup 58 /period put dup 59 /comma put dup 61 /slash put dup 69 /E put dup 72 /H put dup 76 /L put dup 81 /Q put dup 82 /R put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 106 /j put dup 107 /k put dup 110 /n put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec 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cleartomark %%EndFont %%BeginFont: MSBM7 %!PS-AdobeFont-1.1: MSBM7 2.1 %%CreationDate: 1992 Oct 17 08:30:50 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM7) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 78 /N put dup 82 /R put dup 123 /kappa put dup 126 /planckover2pi1 put readonly def /FontBBox{0 -504 2615 1004}readonly def /UniqueID 5032014 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 1 /Delta put dup 3 /Lambda put dup 10 /Omega put dup 33 /exclam put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 58 /colon put dup 59 /semicolon put dup 61 /equal put dup 68 /D put dup 70 /F put dup 73 /I put dup 82 /R put dup 84 /T put dup 91 /bracketleft put dup 93 /bracketright put dup 95 /dotaccent put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 117 /u put dup 119 /w put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 11 /alpha put dup 12 /beta put dup 14 /delta put dup 15 /epsilon1 put dup 17 /eta put dup 18 /theta put dup 21 /lambda put dup 22 /mu put dup 24 /xi put dup 25 /pi put dup 26 /rho put dup 27 /sigma put dup 28 /tau put dup 30 /phi put dup 31 /chi put dup 32 /psi put dup 33 /omega put dup 34 /epsilon put dup 37 /rho1 put dup 39 /phi1 put dup 58 /period put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 62 /greater put dup 64 /partialdiff put dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 74 /J put dup 75 /K put dup 76 /L put dup 77 /M put dup 78 /N put dup 79 /O put dup 80 /P put dup 81 /Q put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 88 /X put dup 90 /Z put dup 97 /a put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 120 /x put dup 121 /y put dup 122 /z put readonly def /FontBBox{-32 -250 1048 750}readonly def /UniqueID 5087385 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D5993DFC0930297866E1CD0A319B6B1FD958 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cleartomark %%EndFont %%BeginFont: CMMI6 %!PS-AdobeFont-1.1: CMMI6 1.100 %%CreationDate: 1996 Jul 23 07:53:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 25 /pi put dup 97 /a put readonly def /FontBBox{11 -250 1241 750}readonly def /UniqueID 5087381 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR6 %!PS-AdobeFont-1.1: CMR6 1.0 %%CreationDate: 1991 Aug 20 16:39:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR6) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR6 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 50 /two put readonly def /FontBBox{-20 -250 1193 750}readonly def /UniqueID 5000789 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR9 %!PS-AdobeFont-1.1: CMR9 1.0 %%CreationDate: 1991 Aug 20 16:39:59 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR9 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 61 /equal put readonly def /FontBBox{-39 -250 1036 750}readonly def /UniqueID 5000792 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI9 %!PS-AdobeFont-1.1: CMMI9 1.100 %%CreationDate: 1996 Jul 23 07:53:55 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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b(to)i(this)f(w)n (orldline)g(is)g(the)h(righ)n(t)e(w)n(edge)h(\(or)f(Rindler)i(w)n (edge\))e Fx(W)3021 535 y Fs(R)3098 523 y Fv(:=)d Fn(f)p Fx(x)h Fn(2)515 623 y Fk(R)575 593 y Fs(4)612 623 y Fn(j)i Fx(x)709 593 y Fs(1)770 623 y Fx(>)c Fn(j)p Fx(x)928 593 y Fs(0)965 623 y Fn(jg)p Fx(:)k Fy(It)h(is)f(the)g(in)n(tersection) g(of)g(the)g(causal)f(future)i(and)f(past)g(of)g(the)h(w)n(orld-)515 722 y(line,)c(or)f(the)g(collection)g(of)g(spacetime)g(p)r(oin)n(ts)g (to)g(whic)n(h)h(the)f(observ)n(er)e(on)i(the)h(w)n(orldline)515 822 y(can)38 b(send)g(signals)f(and)i(from)f(whic)n(h)g(he)h(can)f (also)f(receiv)n(e)g(signals.)68 b(Note)39 b(for)f(later)515 922 y(reference)26 b(that)i(the)g(left)g(w)n(edge)f Fx(W)1656 934 y Fs(L)1725 922 y Fv(:=)22 b Fn(\000)p Fx(W)1978 934 y Fs(R)2058 922 y Fy(is)28 b(the)g(causal)e(complemen)n(t)i(of)p 3092 855 90 4 v 27 w Fx(W)3182 934 y Fs(R)3235 922 y Fy(.)639 1021 y(There)41 b(exists)f(a)g(global)g(co)r(ordinate)g (system)g(on)h Fx(W)2392 1033 y Fs(R)2485 1021 y Fy(that)g(is)g (particularly)e(w)n(ell)515 1121 y(adapted)28 b(to)h(the)g(description) f(of)g(the)h(problem)f(at)h(hand.)40 b(It)29 b(is)f(giv)n(en)g(b)n(y)h (the)g(so-called)515 1220 y(Rindler)e(co)r(ordinates)f Fv(\()p Fx(\034)5 b(;)14 b(u;)g(x)p 1447 1233 48 4 v 21 x Fo(?)1550 1220 y Fv(\))24 b Fn(2)f Fk(R)c Fn(\002)f Fk(R)1906 1190 y Fo(\003)1906 1241 y Fs(+)1979 1220 y Fn(\002)g Fk(R)2122 1190 y Ft(d)p Fo(\000)p Fs(1)2246 1220 y Fy(,)28 b(de\034ned)f(b)n(y)1108 1376 y Fx(x)1155 1342 y Fs(0)1216 1376 y Fv(=)22 b Fx(u)14 b Fv(sinh)f Fx(\034)5 b(;)42 b(x)1679 1342 y Fs(1)1740 1376 y Fv(=)23 b Fx(u)14 b Fv(cosh)e Fx(\034)5 b(;)42 b(x)p 2166 1389 V 21 x Fo(?)2292 1376 y Fv(=)23 b(\()p Fx(x)2459 1388 y Fs(2)2497 1376 y Fx(;)14 b(:)g(:)g(:)f(x)2691 1388 y Ft(d)2731 1376 y Fv(\))p Fx(:)487 b Fy(\(4\))515 1532 y(Here)34 b Fx(\034)44 b Fy(is)34 b(a)g(global)f(time)h(co)r(ordinate)f (on)h(the)h(righ)n(t)f(w)n(edge.)56 b(Note)34 b(that,)i(giv)n(en)e Fx(a)g Fn(2)515 1631 y Fk(R)575 1601 y Fs(+)630 1631 y Fx(;)14 b Fv(\()p Fx(\013)752 1643 y Fs(2)789 1631 y Fx(;)g(:)g(:)g(:)g(\013)990 1643 y Ft(d)1029 1631 y Fv(\))28 b Fn(2)g Fk(R)1232 1601 y Ft(d)p Fo(\000)p Fs(1)1356 1631 y Fy(,)k(the)f(curv)n(e)e Fx(u)f Fv(=)f(1)p Fx(=a)p Fy(,)k Fx(x)p 2131 1644 V 21 x Fo(?)2262 1631 y Fv(=)d(\()p Fx(\013)2440 1643 y Fs(2)2477 1631 y Fx(;)14 b(:)g(:)g(:)g(;)g(\013) 2715 1643 y Ft(d)2754 1631 y Fv(\))31 b Fy(is)f(the)h(w)n(orldline)515 1731 y(of)c(a)f(uniformly)h(accelerated)e(observ)n(er)g(with)j(prop)r (er)e(acceleration)f Fx(a)i Fy(and)g(prop)r(er)f(time)515 1831 y Fx(\033)32 b Fv(=)c Fx(a)731 1800 y Fo(\000)p Fs(1)820 1831 y Fx(\034)9 b Fy(.)48 b(In)31 b(addition,)h(t)n(w)n(o)e (p)r(oin)n(ts)h(in)g(the)g(righ)n(t)g(w)n(edge)f(with)h(the)g(same)g(v) -5 b(alue)31 b(for)515 1930 y(the)24 b Fx(\034)9 b Fy(-co)r(ordinate)23 b(are)g(considered)g(as)h(sim)n(ultaneous)f(in)h(the)g(instan)n (taneous)f(rest)h(frame)515 2030 y(of)30 b(an)n(y)f(suc)n(h)h(observ)n (er)e(\(see)i([Ri]\).)45 b(Among)29 b(the)i(Loren)n(tz)e(b)r(o)r(osts,) h(only)g(the)g(b)r(o)r(osts)g(in)515 2129 y(the)24 b Fx(x)701 2141 y Fs(1)738 2129 y Fy(-direction)f(lea)n(v)n(e)f(the)i (righ)n(t)f(w)n(edge)f(in)n(v)-5 b(arian)n(t.)35 b(In)23 b(inertial)g(co)r(ordinates)f(they)i(are)515 2229 y(giv)n(en)i(b)n(y)i (the)g(linear)e(transformations)1210 2607 y Fx(B)1273 2619 y Ft(\034)1311 2603 y Fg(0)1360 2607 y Fv(=)1447 2316 y Fj(2)1447 2462 y(6)1447 2512 y(6)1447 2561 y(6)1447 2611 y(6)1447 2661 y(6)1447 2714 y(4)1544 2379 y Fv(cosh)13 b Fx(\034)1760 2349 y Fo(0)1872 2379 y Fv(sinh)h Fx(\034)2079 2349 y Fo(0)2190 2379 y Fv(0)83 b Fx(:)14 b(:)g(:)97 b Fv(0)1549 2479 y(sinh)14 b Fx(\034)1756 2449 y Fo(0)1867 2479 y Fv(cosh)f Fx(\034)2083 2449 y Fo(0)2190 2479 y Fv(0)83 b Fx(:)14 b(:)g(:)97 b Fv(0)1644 2579 y(0)281 b(0)181 b(1)83 b Fx(:)14 b(:)g(:)97 b Fv(0)1653 2667 y Fy(.)1653 2700 y(.)1653 2733 y(.)1976 2667 y(.)1976 2700 y(.)1976 2733 y(.)2200 2667 y(.)2200 2700 y(.)2200 2733 y(.)2327 2675 y(.)2359 2700 y(.)2391 2725 y(.)2518 2667 y(.)2518 2700 y(.)2518 2733 y(.)1644 2833 y Fv(0)281 b(0)181 b(0)83 b Fx(:)14 b(:)g(:)97 b Fv(1)2592 2316 y Fj(3)2592 2462 y(7)2592 2512 y(7)2592 2561 y(7)2592 2611 y(7)2592 2661 y(7)2592 2714 y(5)2661 2607 y Fx(:)515 2990 y Fy(In)27 b(the)g(Rindler)g(co)r(ordinates,)f(this)h(b)r(ecomes)g Fx(B)2074 3002 y Ft(\034)2112 2985 y Fg(0)2138 2990 y Fv(\()p Fx(\034)5 b(;)14 b(u;)g(x)p 2333 3003 V 20 x Fo(?)2436 2990 y Fv(\))23 b(=)g(\()p Fx(\034)k Fv(+)17 b Fx(\034)2801 2960 y Fo(0)2825 2990 y Fx(;)d(u;)g(x)p 2947 3003 V 20 x Fo(?)3050 2990 y Fv(\))p Fy(.)37 b(In)27 b(this)515 3089 y(sense,)39 b(the)f(b)r(o)r(osts)e(in)i(the)f Fx(x)1490 3101 y Fs(1)1528 3089 y Fy(-direction)g(act)g(as)f(time)i (translations)e(on)h(the)g(Rindler)515 3189 y(w)n(edge.)639 3289 y(Since)32 b(the)g(\034eld)g(satis\034es)e(the)i(Klein-Gordon)e (equation,)i(one)f(has,)h(in)g(Rindler)f(co-)515 3388 y(ordinates)26 b(on)h Fx(W)1068 3400 y Fs(R)1121 3388 y Fy(:)991 3477 y Fj(\000)1029 3544 y Fx(u)1077 3510 y Fo(\000)p Fs(2)1166 3544 y Fx(@)1215 3510 y Fs(2)1210 3564 y Ft(\034)1270 3544 y Fn(\000)18 b Fx(u)1401 3510 y Fo(\000)p Fs(1)1490 3544 y Fx(@)1534 3556 y Ft(u)1577 3544 y Fx(u@)1669 3556 y Ft(u)1731 3544 y Fv(+)g(\()p Fn(\000)p Fv(\001)1980 3556 y Fo(?)2054 3544 y Fv(+)g Fx(m)2210 3510 y Fs(2)2247 3544 y Fv(\))2279 3477 y Fj(\001)2331 3544 y Fx(Q)p Fv(\()p Fx(\034)5 b(;)14 b(u;)g(x)p 2592 3557 V 21 x Fo(?)2695 3544 y Fv(\))24 b(=)e(0)p Fx(:)370 b Fy(\(5\))515 3699 y(Moreo)n(v)n(er,)29 b(the)j(co)n(v)-5 b(ariance)29 b(of)i(the)h(free)f(\034eld)g(under)g(the)h(P)n (oincar\351)e(group)g(yields,)i(for)515 3799 y(all)27 b Fx(\034)33 b Fn(2)23 b Fk(R)p Fy(,)1393 3899 y Fx(Q)p Fv([)p Fx(f)j Fn(\016)18 b Fx(B)1672 3911 y Fo(\000)p Ft(\034)1766 3899 y Fv(])23 b(=)f(e)1936 3864 y Fs(i)p Ft(L)2001 3872 y Fr(F)2041 3864 y Ft(\034)2082 3899 y Fx(Q)p Fv([)p Fx(f)9 b Fv(]e)2281 3864 y Fo(\000)p Fs(i)p Ft(L)2398 3872 y Fr(F)2437 3864 y Ft(\034)2478 3899 y Fx(;)772 b Fy(\(6\))515 4032 y(with)1362 4132 y Fx(L)1419 4144 y Fs(F)1489 4132 y Fv(=)22 b(d\000\()p Fx(K)6 b Fv(\))p Fx(;)42 b(K)29 b Fv(=)22 b(\012)2127 4097 y Fs(1)p Ft(=)p Fs(2)2232 4132 y Fx(X)2308 4097 y Fs(1)2344 4132 y Fv(\012)2404 4097 y Fs(1)p Ft(=)p Fs(2)2508 4132 y Fx(;)742 b Fy(\(7\))515 4265 y(where)43 b Fx(X)847 4235 y Fs(1)928 4265 y Fy(is)h(the)h(op)r(erator)d(of)i(m)n(ultiplication)g (b)n(y)g Fx(x)2378 4235 y Fs(1)2416 4265 y Fy(.)86 b(In)45 b(particular,)i(for)c Fx(x)51 b Fv(=)515 4364 y(\()p Fx(\034)5 b(;)14 b(u;)g(x)p 710 4377 V 21 x Fo(?)813 4364 y Fv(\))23 b Fn(2)h Fx(W)1025 4376 y Fs(R)1077 4364 y Fy(,)1275 4464 y Fx(Q)p Fv(\()p Fx(\034)5 b(;)14 b(u;)g(x)p 1536 4477 V 21 x Fo(?)1639 4464 y Fv(\))23 b(=)g(e)1819 4430 y Fs(i)p Ft(L)1884 4438 y Fr(F)1923 4430 y Ft(\034)1965 4464 y Fx(Q)p Fv(\(0)p Fx(;)14 b(u;)g(x)p 2227 4477 V 2273 4485 a Fo(?)2329 4464 y Fv(\)e)2398 4430 y Fo(\000)p Fs(i)p Ft(L)2515 4438 y Fr(F)2554 4430 y Ft(\034)2596 4464 y Fx(:)515 4597 y Fy(In)22 b(other)g(w)n(ords,)g Fx(L)1139 4609 y Fs(F)1208 4597 y Fy(generates)e(the)j(free)f(Heisen)n (b)r(erg)f(dynamics)h(of)g(the)h(\034eld)f(op)r(erators)515 4697 y(asso)r(ciated)i(to)h(the)g(righ)n(t)g(w)n(edge.)35 b(Let)26 b(us)f(furthermore)f(in)n(tro)r(duce,)i(for)e(later)h(purp)r (oses,)515 4797 y(the)j(conjugate)e(\034eld)1198 4991 y Fx(P)12 b Fv([)p Fx(f)d Fv(])23 b(:=)1526 4935 y(d)p 1503 4972 92 4 v 1503 5048 a(d)p Fx(\034)1604 4991 y(Q)p Fv([)p Fx(f)k Fn(\016)18 b Fx(B)1884 5003 y Fo(\000)p Ft(\034)1977 4991 y Fv(])24 b Fn(j)2047 5003 y Ft(\034)7 b Fs(=0)2186 4991 y Fv(=)23 b(i)14 b([)p Fx(L)2391 5003 y Fs(F)2437 4991 y Fx(;)g(Q)p Fv([)p Fx(f)9 b Fv(]])k Fx(:)578 b Fy(\(8\))1926 5255 y(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 515 523 a Fy(It)34 b(then)h(follo)n(ws)f(from)g (the)g(basic)g(prop)r(erties)g(of)g(the)h(free)f(\034eld)g(that)h(the)g (equal)f(time)515 623 y(comm)n(utation)27 b(relations)f(of)i(the)f (\034eld)h(and)g(the)g(conjugate)e(\034eld)i(are,)f(at)g Fx(\034)33 b Fv(=)23 b(0)p Fy(,)1126 805 y Fv([)p Fx(Q)p Fv(\(0)p Fx(;)14 b(u;)g(x)p 1411 818 48 4 v 1457 826 a Fo(?)1513 805 y Fv(\))p Fx(;)g(P)e Fv(\(0)p Fx(;)i(u)1806 771 y Fo(0)1829 805 y Fx(;)g(x)p 1866 818 V -34 x Fo(0)1913 826 y(?)1969 805 y Fv(\)])23 b(=)g(i)p Fx(u\016)2243 817 y Ft(u)2286 805 y Fv(\()p Fx(u)2366 771 y Fo(0)2389 805 y Fv(\))28 b Fx(\016)2486 817 y Ft(x)p 2486 828 38 3 v 19 x Fg(?)2577 805 y Fv(\()p Fx(x)p 2609 818 48 4 v 2657 771 a Fo(0)2657 826 y(?)2713 805 y Fv(\))p Fx(:)505 b Fy(\(9\))515 988 y(The)27 b(follo)n(wing)g(useful)h(iden)n(tit)n(y)f (follo)n(ws)g(from)g(\(5\))h(and)f(\(8\):)721 1171 y Fv(i)14 b([)p Fx(L)838 1183 y Fs(F)884 1171 y Fx(;)g(P)e Fv(\(0)p Fx(;)i(u;)g(x)p 1182 1184 V 20 x Fo(?)1285 1171 y Fv(\)])23 b(=)g Fn(\000)1530 1103 y Fj(\000)1567 1171 y Fn(\000)p Fx(u@)1724 1183 y Ft(u)1767 1171 y Fx(u@)1859 1183 y Ft(u)1920 1171 y Fv(+)18 b Fx(u)2051 1136 y Fs(2)2088 1171 y Fv(\()p Fn(\000)p Fv(\001)2254 1183 y Fo(?)2328 1171 y Fv(+)g Fx(m)2484 1136 y Fs(2)2522 1171 y Fv(\))2554 1103 y Fj(\001)2606 1171 y Fx(Q)p Fv(\(0)p Fx(;)c(u;)g(x)p 2868 1184 V 2914 1191 a Fo(?)2970 1171 y Fv(\))p Fx(:)206 b Fy(\(10\))639 1353 y(F)-7 b(or)24 b(an)g(algebraic)e(form)n(ulation)h (of)h(the)h(dynamics,)f(indisp)r(ensable)g(in)h(what)f(follo)n(ws,)515 1453 y(w)n(e)e(need)h(to)g(iden)n(tify)g(the)g(observ)-5 b(able)21 b(algebra)g(of)i(the)g(theory)-7 b(.)35 b(The)23 b(observ)-5 b(able)21 b(algebra)515 1553 y(of)30 b(the)h(\034eld)g(is)g Fn(A)1094 1565 y Fs(F)1170 1553 y Fv(:=)c Fn(f)p Fx(W)12 b Fv(\()p Fx(f)d Fv(\))p Fn(j)p Fx(f)37 b Fn(2)29 b(S)6 b Fv(\()p Fk(R)1864 1522 y Ft(d)p Fs(+1)1987 1553 y Fx(;)14 b Fk(R)p Fv(\))p Fn(g)2158 1522 y Fo(00)2200 1553 y Fy(,)32 b(with)f Fx(W)12 b Fv(\()p Fx(f)d Fv(\))28 b(=)g(e)2809 1522 y Fo(\000)p Fs(i)p Ft(Q)p Fs([)p Ft(f)7 b Fs(])3043 1553 y Fy(the)31 b(usual)515 1652 y(W)-7 b(eyl)33 b(op)r(erators.)51 b(One)33 b(should)g(think)h(of)f(the)g(observ)-5 b(able)32 b(algebra)f(as)h(con)n(taining)g(all)515 1752 y(b)r(ounded)25 b(functions)h(of)f(the)h(\(smeared\))e(\034eld)i(op)r(erators)d Fx(Q)p Fv([)p Fx(f)9 b Fv(])24 b Fy(or,)h(more)g(pictorially)-7 b(,)24 b(all)515 1851 y(observ)-5 b(ables)31 b(that)i(can)g(b)r(e)h (constructed)e(from)h(the)g Fx(Q)p Fv(\()p Fx(x)p Fv(\))p Fy(,)i Fx(x)e Fn(2)g Fk(R)2685 1821 y Ft(d)p Fs(+1)2807 1851 y Fy(.)54 b(Asso)r(ciated)32 b(to)515 1951 y(the)25 b(righ)n(t)f(and)h(left)h(w)n(edges)d(are)h(lo)r(cal)h(algebras)d(of)j (observ)-5 b(ables)24 b Fn(A)2674 1963 y Fs(F;R)p Ft(;)p Fs(L)2872 1951 y Fv(:=)e Fn(f)p Fx(W)12 b Fv(\()p Fx(f)d Fv(\))p Fn(j)p Fx(f)32 b Fn(2)515 2051 y(S)6 b Fv(\()p Fx(W)681 2063 y Fs(R)p Ft(;)p Fs(L)795 2051 y Fx(;)14 b Fk(R)p Fv(\))p Fn(g)966 2021 y Fo(00)1008 2051 y Fy(.)41 b(Again,)29 b(those)g(should)f(b)r(e)i(though)n(t)e(of)h(as)f(con)n (taining)g(all)h(observ)-5 b(ables)515 2150 y(that)33 b(can)f(b)r(e)h(constructed)f(with)i(the)f(\034eld)g(op)r(erators)e Fx(Q)p Fv(\()p Fx(x)p Fv(\))p Fy(,)k(for)d Fx(x)h Fy(b)r(elonging)f(to) h(the)515 2250 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b(results)h(extend)g(without)h(problem)f(to)g (an)g Fx(N)9 b Fy(-lev)n(el)28 b(system,)i(at)f(the)h(cost)515 3183 y(of)35 b(irrelev)-5 b(an)n(t)34 b(notational)g(complications.)58 b(So)35 b(w)n(e)g(follo)n(w)f(the)i(ph)n(ysics)e(literature)g(on)515 3283 y(the)40 b(sub)5 b(ject)40 b(and)g(limit)h(ourselv)n(es)d(to)i(a)g (highly)f(idealized)h(t)n(w)n(o-lev)n(el)e(detector.)74 b(Its)515 3383 y(observ)-5 b(able)20 b(algebra)g(is)h(simply)h(the)g (algebra)d(of)j(t)n(w)n(o)f(b)n(y)g(t)n(w)n(o)g(matrices)f Fn(B)s Fv(\()p Fk(C)2932 3353 y Fs(2)2969 3383 y Fv(\))p Fy(.)35 b(It)22 b(will)g(b)r(e)515 3482 y(con)n(v)n(enien)n(t)e(to)h (use)g(a)g(represen)n(tation)f(of)h(this)h(algebra)e(in)h(whic)n(h)g(b) r(oth)h(the)g(ground)e(state)515 3582 y(and)28 b(the)h(Gibbs)g(state)g (at)f(in)n(v)n(erse)g(temp)r(erature)g Fx(\014)33 b Fy(are)28 b(represen)n(ted)f(b)n(y)h(v)n(ectors.)39 b(This)515 3682 y(represen)n(tation,)28 b(w)n(ell)h(kno)n(wn)g(in)g(the)h 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b(ables)32 b(of)515 1174 y(the)c(coupled)f(system)g(are)665 1391 y Fv(\()p Ff(2)18 b Fv(+)g Fx(m)933 1356 y Fs(2)970 1391 y Fv(\))p Fx(Q)p Fv(\()p Fx(x)p Fv(\))84 b(=)f Fn(\000)p Fx(\025\032)p Fv(\()p Fx(x)1646 1403 y Fo(\003)1685 1391 y Fv(\)\()p Fx(A)19 b Fv(+)f Fx(A)1975 1356 y Fo(y)2010 1391 y Fv(\)\()2084 1335 y Fx(\034)9 b Fv(\()p Fx(x)p Fv(\))p 2084 1372 158 4 v 2142 1448 a Fx(a)2252 1391 y Fv(\))947 b Fy(\(15\))1034 1573 y Fv(_)1003 1594 y Fx(A)p Fv(\()p Fx(\033)s Fv(\))84 b(=)f Fn(\000)p Fv(i)p Fx(E)5 b(A)p Fv(\()p Fx(\033)s Fv(\))19 b(+)f(i)p Fx(\025C)6 b Fv(\()p Fx(\033)s Fv(\))2107 1481 y Fj(Z)2206 1594 y Fv(d)p Fx(u)p Fv(d)p Fx(x)p 2346 1607 48 4 v 21 x Fo(?)2449 1594 y Fx(au)27 b(\032)p Fv(\()p Fx(x)2690 1606 y Fo(\003)2729 1594 y Fv(\))p Fx(Q)p Fv(\()p Fx(a\033)n(;)14 b(u;)g(x)p 3070 1607 V 3118 1615 a Fo(?)3174 1594 y Fv(\))p Fx(;)515 1804 y Fy(The)38 b(function)g Fx(\032)g Fy(tunes)g(the)g(coupling)f(b)r (et)n(w)n(een)g(the)i(detector)e(and)g(the)h(\034eld.)68 b(It)38 b(is)515 1904 y(ev)-5 b(aluated)27 b(at)1574 2004 y Fx(x)1621 2016 y Fo(\003)1682 2004 y Fv(:=)c Fx(x)c Fn(\000)f Fx(x)p Fv(\()p Fx(\034)9 b Fv(\()p Fx(x)p Fv(\))p Fx(=a)p Fv(\))p Fx(;)515 2147 y Fy(the)30 b(spacelik)n(e)f(v)n(ector)g (linking)h Fx(x)h Fy(in)f(the)h(righ)n(t)e(w)n(edge)h(to)g(the)g (instan)n(taneous)f(p)r(osition)515 2247 y Fx(x)p Fv(\()p Fx(\033)s Fv(\))d Fy(of)g(the)f(detector,)g(at)g(prop)r(er)g(time)g Fx(\033)i Fv(=)22 b Fx(\034)9 b Fv(\()p Fx(x)p Fv(\))p Fx(=a)p Fy(,)27 b(where)e Fx(\034)9 b Fv(\()p Fx(x)p Fv(\))27 b Fy(is)e(the)g(Rindler)h(time)515 2347 y(co)r(ordinate)g (de\034ned)i(in)g(\(4\).)639 2446 y(Let)23 b Fv(\()p Fx(\034)5 b(;)14 b(u;)g(x)p 978 2459 V 1026 2467 a Fo(?)1082 2446 y Fv(\))23 b Fy(b)r(e)g(the)h(Rindler)f(co)r(ordinates)e(of)i(the) h(p)r(oin)n(t)f Fx(x)g Fy(then)h(the)f(ones)g(of)g Fx(x)p Fv(\()p Fx(\033)s Fv(\))515 2546 y Fy(are)34 b Fv(\()p Fx(\034)5 b(;)14 b Fv(1)p Fx(=a;)g Fv(0)p 936 2559 42 4 v 977 2567 a Fo(?)1033 2546 y Fv(\))36 b Fy(and)f(hence)h(w)n(e)f(ma) n(y)g(iden)n(tify)h Fx(x)2184 2558 y Fo(\003)2223 2546 y Fy(,)i(whose)d(co)r(ordinates)f(are)g Fv(\(0)p Fx(;)14 b(u)23 b Fn(\000)515 2645 y Fv(1)p Fx(=a;)14 b(x)p 680 2658 48 4 v 726 2666 a Fo(?)782 2645 y Fv(\))p Fy(,)24 b(with)e(an)g(elemen)n(t)g(of)g Fv(\()p Fn(\000)p Fv(1)p Fx(=a;)14 b Fv(+)p Fn(1)p Fv(\))7 b Fn(\002)g Fk(R)2125 2615 y Ft(d)p Fo(\000)p Fs(1)2248 2645 y Fy(.)35 b(W)-7 b(e)22 b(tak)n(e)g(the)g(coupling)g(function)515 2745 y Fx(\032)h Fy(to)g(b)r(e)h(in)g Fx(C)945 2715 y Fo(1)939 2766 y Fs(0)1016 2745 y Fv(\(\()p Fn(\000)p Fv(1)p Fx(=a;)14 b Fv(+)p Fn(1)p Fv(\))c Fn(\002)g Fk(R)1635 2715 y Ft(d)p Fo(\000)p Fs(1)1757 2745 y Fv(\))p Fy(,)25 b(normalized)d(as)2355 2678 y Fj(R)2424 2745 y Fx(\032)p Fv(\()p Fx(x)p 2499 2758 V 1 w Fv(\)d)p Fx(x)p 2625 2758 V 2673 2715 a Ft(d)2734 2745 y Fv(=)h(1)p Fy(.)35 b(T)n(ypically)22 b(w)n(e)515 2845 y(imagine)g Fx(\032)h Fy(to)f(b)r(e)h(p)r(eak)n(ed)f(at)h(the)g 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Fn(\001)g Fx(Q)p Fv(\()p Fx(g)s Fv(\))g(+)g Fx(G)1744 593 y Fo(\003)1797 623 y Fn(\001)g Fx(Q)p Fv(\()p 1932 577 43 4 v Fx(g)r Fv(\))p Fy(,)27 b(and)e(for)g(sums)g(of)g(suc)n(h)g(terms,)h(where)f Fx(G)515 722 y Fy(are)c(matrices)g(acting)h(on)g(the)h(detector)e (space,)i(and)f Fx(g)k Fn(2)d Fx(L)2382 692 y Fs(2)2419 722 y Fv(\()p Fk(R)2511 692 y Fs(3)2549 722 y Fx(;)14 b Fv(d)p Fx(x)p 2632 735 48 4 v Fv(\))23 b Fy(are)e(\020form)g (factors\021.)639 822 y(The)28 b(follo)n(wing)e(result)i(is)f(pro)n(v)n (ed)f(in)i(Section)f(5.)515 1005 y Fm(Prop)s(osition)j(2.1)40 b Fw(The)c(op)l(er)l(ator)1709 984 y Fj(e)1701 1005 y Fx(L)1758 1017 y Ft(\025)1836 1005 y Fw(in)f(\(16\))h(is)f(for)h(al)t (l)g Fx(\025)f Fw(essential)t(ly)h(self-adjoint)515 1120 y(on)e Fx(D)r Fv(\()p Fx(L)798 1132 y Fs(0)835 1120 y Fv(\))22 b Fn(\\)g Fx(D)r Fv(\()p Fx(I)7 b Fv(\))35 b Fw(and)g(the)g(maps)f Fx(\013)1761 1090 y Ft(\025)1761 1141 y(\033)1806 1120 y Fv(\()p Fx(B)t Fv(\))e(:=)f(e)2125 1090 y Fs(i)2150 1075 y 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2037 1959 a Fo(?)2094 1938 y Fn(j)2117 1904 y Fs(2)2172 1938 y Fv(+)18 b Fx(m)2328 1904 y Fs(2)2365 1938 y Fv(\))2397 1904 y Fs(1)p Ft(=)p Fs(2)2516 1938 y Fv(sinh)c Fk({)s Fx(;)g(k)p 2773 1951 V 2819 1959 a Fo(?)2875 1871 y Fj(\001)2913 1938 y Fx(;)295 b Fy(\(17\))515 2144 y(where)18 b Fj(b)g Fy(denotes)27 b(the)h(F)-7 b(ourier)27 b(transform.)515 2310 y Fm(Theorem)k(2.2)41 b Fw(L)l(et)f Fx(d)j Fn(\025)g Fv(1)d Fw(if)h Fx(m)i(>)g Fv(0)d Fw(and)h Fx(d)i Fn(\025)g Fv(2)d Fw(if)i Fx(m)g Fv(=)h(0)p Fw(,)g(and)f(supp)l(ose)f(the)515 2409 y(fol)t(lowing)32 b(\020F)-6 b(ermi)30 b(Golden)h(R)n(ule)e (Condition)-8 b(\021)37 b(holds,)1035 2517 y Fj(Z)1081 2705 y Fu(R)1141 2630 y Fv(d)p Fk({)d Fv(e)1313 2595 y Fo(\000)p Fs(i)1393 2573 y Fi(E)p 1393 2582 44 3 v 1399 2615 a(a)1447 2595 y Fu({)1528 2630 y Fx(g)s Fv(\()p Fk({)s Fx(;)14 b(k)p 1698 2643 46 4 v 1745 2650 a Fo(?)1801 2630 y Fv(\))23 b Fn(6)p Fv(=)g(0)118 b Fw(for)31 b(some)f Fx(k)p 2449 2643 V 2495 2650 a Fo(?)2574 2630 y Fn(2)23 b 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y(Mor)l(e)j(gener)l(al)t(ly,)g(if)g Fx(\045)e Fw(is)i(any)f(density)g(matrix)f(on)h Fn(H)h Fw(then)942 3640 y Fv(lim)913 3689 y Ft(\033)r Fo(!1)1100 3640 y Fv(T)p Fx(r)16 b(\045\013)1309 3605 y Ft(\025)1309 3660 y(\033)1354 3640 y Fv(\()p Fx(B)t(F)c Fv(\))24 b(=)1661 3547 y Fj(\020)1786 3583 y Fv(1)p 1721 3620 172 4 v 1721 3697 a Fx(Z)1778 3709 y Ft(\014)s(;)p Fs(D)1902 3640 y Fv(T)-7 b(r)29 b(e)2054 3605 y Fo(\000)p Ft(\014)s(H)2201 3613 y Fr(D)2251 3640 y Fx(B)2318 3547 y Fj(\021)2382 3640 y Fn(h)p Fv(0)p Fn(j)p Fx(F)12 b Fn(j)p Fv(0)p Fn(i)18 b Fv(+)g Fx(O)r Fv(\()p Fx(\025)2887 3605 y Fs(2)2925 3640 y Fv(\))p Fx(;)251 b Fy(\(20\))515 3879 y Fw(for)30 b(any)g(dete)l(ctor)g(observable)i Fx(B)27 b Fn(2)d(B)s Fv(\()p Fk(C)1836 3849 y Fs(2)1872 3879 y Fv(\))30 b Fw(and)g(any)g(\034eld)h(observable)g Fx(F)k Fn(2)24 b(A)3061 3891 y Fs(F)3108 3879 y Fw(.)515 4045 y Fy(Result)29 b(\(19\))f(sho)n(ws)g(that)h(if)g(at)f Fx(\033)h Fv(=)24 b(0)k 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(the)g(equilibrium)g(state)515 4842 y Fn(j)p Fx(\025)p Fn(i)h(2)f(H)j Fy(of)g(the)g(coupled)f(system,)h(see)f(also)f(\(28\))h (b)r(elo)n(w.)36 b(An)26 b(expansion)e(of)i Fn(h)p Fx(\025)p Fn(j)15 b(\001)f(j)p Fx(\025)p Fn(i)27 b Fy(for)515 4942 y(small)h Fx(\025)h Fy(yields)f(the)h(uncoupled)f(equilibrium)g(state)h (plus)f(an)g(error)f(of)h(second)g(order)f(in)1926 5255 y(9)p eop end %%Page: 10 10 TeXDict begin 10 9 bop 515 523 a Fx(\025)26 b Fy(\(the)f(absence)g(of)g (a)g(\034rst)g(order)f(error)f(term)i(is)h(due)f(to)g(the)h(fact)f (that)h(the)f(exp)r(ectation)515 623 y(of)i(the)h(in)n(teraction)f Fx(I)34 b Fy(in)28 b(the)g(uncoupled)g(equilibrium)f(state)h(v)-5 b(anishes\).)639 722 y(2\))28 b(The)f(approac)n(h)f(to)h(the)h(limit)h (state)e(in)h(\(19\))f(is)g(exp)r(onen)n(tially)g(fast,)1243 850 y Fj(\014)1243 900 y(\014)1270 920 y Fv(T)p Fx(r)17 b(\045\013)1480 886 y Ft(\025)1480 941 y(\033)1525 920 y Fv(\()p Fx(B)t Fv(\))i Fn(\000)f(h)p Fx(\025)p Fn(j)p Fx(B)t Fn(j)p Fx(\025)p 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3039 y Fv(\))p Fx(\032)1063 3051 y Fo(?)1119 3039 y Fv(\()p Fx(x)p 1151 3052 V 1199 3059 a Fo(?)1255 3039 y Fv(\))p Fw(,)34 b(\(\020squar)l(e)e(dete)l(ctor\021\))h(with)g Fx(\032)2278 3051 y Fs(1)2343 3039 y Fn(\025)28 b Fv(0)p Fw(.)47 b(Then)33 b(c)l(ondition)g(\(18\))h(is)515 3138 y(satis\034e)l(d)25 b(for)g(al)t(l)h Fx(E)k Fw(exc)l(ept)25 b(for)g Fx(E)j Fn(2)c(E)7 b Fw(,)26 b(wher)l(e)g Fn(E)32 b Fw(is)25 b(a)g(discr)l(ete)g(\(p)l(ossibly)i(empty\))e(subset)515 3238 y(of)30 b Fk(R)p Fw(.)39 b(In)29 b(p)l(articular,)i Fx(\030)t Fv(\()p Fx(E)5 b Fv(\))24 b Fx(>)f Fv(0)29 b Fw(for)i(al)t(l)f Fx(E)f Fn(62)23 b(E)7 b Fw(.)639 3404 y Fy(V)-7 b(alues)26 b(of)g Fx(E)31 b Fy(satisfying)25 b Fx(\030)t Fv(\()p Fx(E)5 b Fv(\))24 b(=)f(0)i Fy(\(whic)n(h)h(form)g (necessarily)e(a)h(subset)h(of)g Fn(E)34 b Fy(in)26 b(the)515 3503 y(prop)r(osition\))31 b(corresp)r(ond)f(to)h(energy)g(gaps)g(of)g (the)h(detector)g(Hamiltonian)f(for)g(whic)n(h)515 3603 y(thermalization)26 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y(Let)38 b(us)f(consider)f Fx(\026)1297 1791 y Fs(0)1374 1779 y Fv(=)i(1)p Fy(;)k(a)37 b(simple)g(mo)r(di\034cation)g(of)g(the)h (follo)n(wing)e(argumen)n(t)515 1878 y(yields)e(the)i(general)d(case.) 58 b(Assume)35 b Fw(ad)i(absur)l(dum)e Fy(that)g Fx(J)8 b Fv(\(0)p Fx(;)14 b(\026)p Fv(\))36 b(=)f(0)f Fy(for)h(all)f Fx(\026)h Fy(in)g(a)515 1978 y(neigh)n(b)r(ourho)r(o)r(d)26 b(of)i Fv(1)p Fy(.)36 b(Then,)28 b(b)n(y)f(taking)g(deriv)-5 b(aties)27 b(of)g Fx(J)8 b Fv(\(0)p Fx(;)14 b(\026)p Fv(\))28 b Fy(with)g(resp)r(ect)f(to)h Fx(\026)p Fy(,)f(at)515 2078 y Fx(\026)565 2090 y Fs(0)625 2078 y Fv(=)c(1)p Fy(,)k(w)n(e)g(see)g(that)1246 2185 y Fj(Z)1293 2374 y Fu(R)1353 2298 y Fv(d)p Fx(y)j Fv(\(1)18 b(+)g Fx(y)1689 2264 y Fs(2)1726 2298 y Fv(\))1758 2264 y Fo(\000)p Ft(n)1869 2298 y Fv(\(1)h(+)f Fx(y)2089 2264 y Fs(2)2126 2298 y Fv(\))2158 2264 y Fo(\000)p Fs(1)p Ft(=)p Fs(2)2314 2298 y Fx(f)9 b Fv(\()p Fx(y)s Fv(\))23 b(=)g(0)p Fx(;)583 b Fy(\(23\))515 2522 y(for)31 b(all)h Fx(n)f Fv(=)g(0)p Fx(;)14 b Fv(1)p Fx(;)g(:)g(:)g(:)31 b Fy(No)n(w,)i(it)f(is)h(not)f (di\036cult)h(to)f(v)n(erify)g(that)g(the)h(linear)e(span)h(of)g(all) 515 2622 y(functions)37 b Fv(\(1)24 b(+)g Fx(y)1113 2592 y Fs(2)1150 2622 y Fv(\))1182 2592 y Fo(\000)p Ft(n)1280 2622 y Fy(,)39 b Fx(n)f Fv(=)g(1)p Fx(;)14 b Fv(2)p Fx(;)g(:)g(:)g(:)35 b Fy(is)i(dense)g(in)g(the)g(space)f(of)h(ev)n(en)f(functions)h(in)515 2721 y Fx(L)572 2691 y Fs(2)608 2721 y Fv(\()p Fk(R)p Fx(;)14 b(dy)s Fv(\))p Fy(.)70 b(\(One)38 b(ma)n(y)g(pro)n(v)n(e)e (this)j(with)g(little)g(e\033ort)f(via)f(the)i(F)-7 b(ourier)37 b(transform,)515 2821 y(for)d(example.\))57 b(It)35 b(th)n(us)f(follo)n (ws)g(from)g(\(23\))g(that)g(the)h(ev)n(en)f(part)g(of)h Fx(f)43 b Fy(m)n(ust)34 b(v)-5 b(anish,)515 2921 y Fx(f)9 b Fv(\()p Fx(y)s Fv(\))18 b(+)g Fx(f)9 b Fv(\()p Fn(\000)p Fx(y)s Fv(\))23 b(=)f(0)27 b Fy(for)g(all)h Fx(y)d Fn(\025)e Fv(0)p Fy(.)36 b(In)28 b(particular,)e Fx(f)9 b Fv(\(0\))23 b(=)g(0)p Fy(,)k(whic)n(h)h(means)f(that)1676 3103 y Fx(a)1720 3069 y Fo(\000)p Fs(1)1832 3103 y Fv(=)c Fn(\000)p Fv(i)17 b Fj(b)-63 b Fx(\032)2051 3115 y Fs(1)2088 3064 y Fo(0)2111 3103 y Fv(\(0\))1014 b Fy(\(24\))515 3286 y(\(w)n(e)25 b(assume)f(without)i(loss)f(of)g(generalit)n(y)f(that)h Fx(\032)2107 3298 y Fs(1)2170 3286 y Fy(is)g(normalized)f(as)2773 3219 y Fj(R)2812 3315 y Fu(R)2872 3286 y Fv(d)p Fx(x)14 b(\032)3022 3298 y Fs(1)3059 3286 y Fv(\()p Fx(x)p Fv(\))25 b(=)d(1)p Fy(\).)515 3396 y(On)38 b(the)h(other)f(hand,)k(w)n(e)c(ha)n (v)n(e)f Fn(\000)p Fv(i)17 b Fj(b)-63 b Fx(\032)1757 3408 y Fs(1)1794 3356 y Fo(0)1818 3396 y Fv(\(0\))41 b(=)g Fn(\000)2150 3329 y Fj(R)2189 3425 y Fu(R)2249 3396 y Fv(d)p Fx(x)14 b(x\032)2446 3408 y Fs(1)2484 3396 y Fv(\()p Fx(x)p Fv(\))43 b Fx(<)e(a)2788 3365 y Fo(\000)p Fs(1)2877 3396 y Fy(,)g(since)e(in)g(the)515 3495 y(in)n(tegral,)22 b Fx(x)i(>)e Fn(\000)p Fx(a)1103 3465 y Fo(\000)p Fs(1)1215 3495 y Fy(due)h(to)g(the)g(fact)g(that)g Fx(\032)1979 3507 y Fs(1)2039 3495 y Fy(is)g(supp)r(orted)g(in)g Fv(\()p Fn(\000)p Fv(1)p Fx(=a;)14 b Fn(1)p Fv(\))p Fy(.)34 b(Therefore)515 3595 y(condition)27 b(\(24\))g(is)h(not)f(v)n(eri\034ed.)639 3694 y(This)h(sho)n(ws)f(that)i(giv)n(en)e(an)n(y)g Fx(\026)1673 3706 y Fs(0)1734 3694 y Fx(>)d Fv(0)k Fy(w)n(e)f(can)h(\034nd)g(a)g Fx(\026)2454 3706 y Fs(1)2515 3694 y Fx(>)c Fv(0)k Fy(\(arbitrarily)e (close)h(to)515 3794 y Fx(\026)565 3806 y Fs(0)602 3794 y Fy(\))h(with)g(the)g(prop)r(ert)n(y)e(that)i Fx(J)8 b Fv(\(0)p Fx(;)14 b(\026)1728 3806 y Fs(1)1765 3794 y Fv(\))24 b Fn(6)p Fv(=)e(0)p Fy(.)639 3894 y(Pic)n(k)d(a)f(nonzero)f Fx(K)1247 3906 y Fs(0)1306 3894 y Fn(2)24 b Fk(R)1445 3864 y Ft(d)p Fo(\000)p Fs(1)1587 3894 y Fy(satisfying)h Fj(c)-91 b Fx(\032)1990 3906 y Fo(?)2046 3894 y Fv(\()p Fx(K)2149 3906 y Fs(0)2186 3894 y Fv(\))24 b Fn(6)p Fv(=)e(0)c Fy(and)h(set)f Fx(\026)2712 3906 y Fs(0)2772 3894 y Fv(:=)2883 3823 y Fj(p)p 2966 3823 403 4 v 71 x Fn(j)p Fx(K)3060 3906 y Fs(0)3097 3894 y Fn(j)3120 3870 y Fs(2)3176 3894 y Fv(+)g Fx(m)3332 3870 y Fs(2)3369 3894 y Fy(.)515 3993 y(Then,)40 b(b)n(y)e(the)g(ab)r(o)n(v)n(e)f(argumen)n(t)f(and)i(b)n(y)g (the)g(con)n(tin)n(uit)n(y)f(of)46 b Fj(c)-91 b Fx(\032)2674 4005 y Fo(?)2768 3993 y Fy(there)38 b(is)f(a)h Fx(\026)3214 4005 y Fs(1)3291 3993 y Fv(=:)515 4022 y Fj(p)p 598 4022 V 71 x Fn(j)p Fx(K)692 4105 y Fs(1)729 4093 y Fn(j)752 4069 y Fs(2)807 4093 y Fv(+)18 b Fx(m)963 4069 y Fs(2)1020 4093 y Fy(\(whic)n(h)i(is)f(close)g(to)g Fx(\026)1691 4105 y Fs(0)1748 4093 y Fy(and)g(de\034nes)g(a)g Fx(K)2297 4105 y Fs(1)2354 4093 y Fy(close)f(to)i Fx(K)2709 4105 y Fs(0)2745 4093 y Fy(\))g(s.t.)35 b Fx(J)8 b Fv(\(0)p Fx(;)14 b(\026)3158 4105 y Fs(1)3195 4093 y Fv(\))23 b Fn(6)p Fv(=)f(0)515 4193 y Fw(and)30 b Fj(c)-91 b Fx(\032)711 4205 y Fo(?)767 4193 y Fv(\()p Fx(K)870 4205 y Fs(1)907 4193 y Fv(\))23 b Fn(6)p Fv(=)g(0)p Fy(.)34 b(Hence)22 b(w)n(e)f(ha)n(v)n(e)g(sho)n(wn)g(that)g(there)h(exists)f(a)g(nonzero)f Fx(K)2978 4205 y Fs(1)3037 4193 y Fy(satisfying)515 4292 y Fv(i)8 b Fj(c)-91 b Fx(\032)581 4304 y Fo(?)637 4292 y Fv(\()p Fx(K)740 4304 y Fs(1)777 4292 y Fv(\))p Fx(J)8 b Fv(\(0)p Fx(;)14 b(!)1026 4304 y Fs(1)1063 4292 y Fv(\))23 b Fn(6)p Fv(=)g(0)p Fy(,)h(where)f Fx(!)1583 4304 y Fs(1)1643 4292 y Fv(=)1730 4221 y Fj(p)p 1813 4221 V 71 x Fn(j)p Fx(K)1907 4304 y Fs(1)1944 4292 y Fn(j)1967 4268 y Fs(2)2023 4292 y Fv(+)18 b Fx(m)2179 4268 y Fs(2)2216 4292 y Fy(.)36 b(Condition)23 b(\(18\))g(is)h(th)n(us)g(satis\034ed)515 4392 y(for)j Fx(E)h Fv(=)23 b(0)p Fy(.)639 4491 y(Finally)g(w)n(e)g (pass)f(to)h(the)h(other)e(v)-5 b(alues)23 b(of)g Fx(E)29 b Fy(b)n(y)22 b(an)h(analyticit)n(y)g(argumen)n(t.)34 b(Indeed,)515 4591 y(one)j(easily)g(sees)g(\(b)r(est)i(b)n(y)f(using)f (the)h(form)g(of)g Fx(J)46 b Fy(in)38 b(whic)n(h)f(one)h(in)n(tegrates) e(o)n(v)n(er)g Fk({)515 4691 y Fy(rather)31 b(than)h Fx(y)s Fy(,)h(c.f.)51 b(\(17\),)33 b(\(18\)\))f(that)h(the)f(map)h Fx(E)i Fn(7!)c Fx(J)8 b Fv(\()p Fx(E)d(;)14 b(!)2615 4703 y Fs(1)2652 4691 y Fv(\))33 b Fy(is)f(analytic)f(and)h(b)n(y)515 4790 y(the)24 b(previous)f(argumen)n(t)g(it)h(do)r(es)g(not)g(v)-5 b(anish)23 b(at)h Fx(E)k Fv(=)23 b(0)p Fy(.)35 b(Th)n(us)24 b(the)g(zero)r(es)f(of)h(this)g(map)515 4890 y(are)f(con)n(tained)h(in) g(a)g(discrete)g(set)h Fn(E)7 b Fv(\()p Fx(!)1746 4902 y Fs(1)1783 4890 y Fv(\))23 b Fn(\032)g Fk(C)p Fy(.)36 b(An)n(y)24 b Fx(E)30 b Fy(a)n(v)n(oiding)22 b(this)j(set)g(th)n(us)f (satis\034es)515 4990 y(\(18\).)2628 b Fh(\004)1905 5255 y Fy(11)p eop end %%Page: 12 12 TeXDict begin 12 11 bop 515 523 a Fz(3)131 b(Pro)t(of)43 b(of)h(Theorem)f(2.2)515 721 y Fl(3.1)112 b(Strategy)515 875 y Fy(As)27 b(men)n(tioned)h(in)f(the)h(in)n(tro)r(duction,)f(the)h (\034rst)f(ingredien)n(t)g(of)g(the)h(pro)r(of)f(is)g(the)h(obser-)515 974 y(v)-5 b(ation)26 b(that)h(the)f(Mink)n(o)n(wski)f(v)-5 b(acuum)27 b(is)f(\(a)g(realization)f(of)6 b(\))27 b(the)g(GNS)g (represen)n(tation)515 1074 y(of)e(a)f(KMS)h(state)g(on)g(the)g(righ)n (t)g(w)n(edge)f(algebra)f(for)h(the)i(Loren)n(tz)e(b)r(o)r(osts)g(at)h (the)h(in)n(v)n(erse)515 1174 y(temp)r(erature)36 b Fx(\014)44 b Fv(=)38 b(2)p Fx(\031)s Fy(.)66 b(This)37 b(is)g(the)h(con)n(ten)n(t) e(of)i(Theorem)e(3.1)g(b)r(elo)n(w.)65 b(T)-7 b(o)37 b(giv)n(e)f(a)515 1273 y(precise)25 b(statemen)n(t,)i(w)n(e)f(need)h (the)g(so-called)e(mo)r(dular)h(conjugation)g(op)r(erator,)f(de\034ned) 515 1373 y(as)i(follo)n(ws:)857 1546 y Fx(J)903 1558 y Fs(F)973 1546 y Fv(=)c(\000\()p Fx(j)1179 1566 y Fr(F)1223 1546 y Fv(\))p Fx(;)42 b Fv(where)27 b Fn(8)h Fx( )e Fn(2)d Fx(L)1849 1511 y Fs(2)1886 1546 y Fv(\()p Fk(R)1978 1511 y Ft(d)2017 1546 y Fx(;)14 b Fv(d)p Fx(x)p 2100 1559 48 4 v 1 w Fv(\))p Fx(;)41 b(j)2278 1566 y Fr(F)2323 1546 y Fx( )s Fv(\()p Fx(x)p 2412 1559 V 1 w Fv(\))23 b(=)p 2603 1478 58 4 v 23 w Fx( )s Fv(\()p Fn(\000)p Fx(x)2804 1558 y Fs(1)2841 1546 y Fx(;)14 b(x)p 2878 1559 48 4 v 2926 1566 a Fo(?)2982 1546 y Fv(\);)194 b Fy(\(25\))515 1718 y(here)27 b Fv(\000\()p Fx(j)5 b Fv(\))28 b Fy(stands)f(for)g(the)h(second)f(quan)n(tization)f(of)i Fx(j)5 b Fy(.)515 1891 y Fm(Theorem)31 b(3.1)g(\([BiWi)n(]\))41 b Fw(The)26 b(F)-6 b(o)l(ck)25 b(vacuum)g(in)f Fn(F)33 b Fw(induc)l(es)25 b(on)g Fn(A)2774 1903 y Fs(F)p Ft(;)p Fs(R)2914 1891 y Fw(a)g(state)f(which)515 1991 y(is)30 b(KMS)f(at)h(inverse)g(temp)l(er)l(atur)l(e)f Fx(\014)f Fv(=)22 b(2)p Fx(\031)33 b Fw(for)d Fx(\013)2126 1961 y Fs(0)2126 2014 y(F)p Ft(;\034)2231 1991 y Fw(.)38 b(In)30 b(p)l(articular,)h(one)f(has)734 2185 y Fn(A)800 2151 y Fo(0)800 2206 y Fs(F)p Ft(;R)941 2185 y Fv(=)22 b Fn(A)1094 2197 y Fs(F)p Ft(;L)1207 2185 y Fx(;)99 b(J)1375 2197 y Fs(F)1422 2185 y Fn(A)1488 2197 y Fs(F)p Ft(;R)1605 2185 y Fx(J)1651 2197 y Fs(F)1721 2185 y Fv(=)23 b Fn(A)1875 2197 y Fs(F)p Ft(;L)1987 2185 y Fx(;)p 2109 2113 372 4 v 99 w Fn(A)2175 2197 y Fs(F)p Ft(;R)2292 2185 y Fn(j)p Fv(0)p Fx(;)14 b Fv(F)p Fn(i)23 b Fv(=)g Fn(F)31 b Fv(=)p 2770 2113 367 4 v 23 w Fn(A)2836 2197 y Fs(F)p Ft(;L)2948 2185 y Fn(j)p 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Fx(\014)t(;)14 b Fv(D)p Fn(i)23 b Fy(in)n(tro)r(duced)e(in)h(Section)g(2.2)e(are)h (GNS)h(represen)n(tativ)n(es)515 2944 y(of)i(the)h(KMS)g(states)f(at)g (in)n(v)n(erse)f(temp)r(erature)h Fx(\014)29 b Fy(for)24 b(the)h(free)f(detector)g(dynamics)g Fx(\013)3264 2956 y Fs(D)p Ft(;\033)515 3044 y Fy(on)32 b(the)h(detector)f(observ)-5 b(able)31 b(algebra)g Fn(B)s Fv(\()p Fk(C)1966 3014 y Fs(2)2002 3044 y Fv(\))p Fy(.)53 b(This)32 b(w)n(ell)g(kno)n(wn)g (observ)-5 b(ation)31 b(is)i(for)515 3143 y(con)n(v)n(enience)i (summarized)h(in)h(the)g(follo)n(wing)f(lemma.)64 b(The)37 b(appropriate)e(conjugate)515 3243 y(op)r(erator)26 b(is)h(giv)n(en)g (b)n(y)1649 3343 y Fx(J)1695 3355 y Fs(D)1772 3343 y Fv(=)22 b Fx(E)5 b Fv(\()p Fx(C)26 b Fn(\012)18 b Fx(C)6 b Fv(\))p Fx(;)515 3486 y Fy(where)29 b Fx(C)37 b Fy(is)30 b(the)g(an)n(tilinear)f(op)r(erator)g(of)h(complex)f(conjugation)g(on)h Fk(C)2850 3456 y Fs(2)2918 3486 y Fy(and)f Fx(E)36 b Fy(is)30 b(the)515 3586 y(exc)n(hange)c(op)r(erator)g(on)h Fk(C)1380 3556 y Fs(2)1436 3586 y Fn(\012)18 b Fk(C)1579 3556 y Fs(2)1616 3586 y Fy(,)27 b Fx(E)5 b(')19 b Fn(\012)f Fx(\037)23 b Fv(=)g Fx(\037)18 b Fn(\012)g Fx(')p Fy(.)515 3744 y Fm(Lemma)31 b(3.2)41 b Fw(F)-6 b(or)30 b(any)h Fx(\014)d(>)23 b Fv(0)p Fw(,)31 b(the)f(ve)l(ctor)g Fn(j)p Fx(\014)t(;)14 b Fv(D)p Fn(i)31 b Fw(induc)l(es)g(on)f Fn(B)s Fv(\()p Fk(C)2778 3714 y Fs(2)2815 3744 y Fv(\))g Fw(a)h(state)e(that)i(is)515 3844 y(KMS)e(at)h(inverse)g(temp)l(er)l (atur)l(e)f Fx(\014)34 b Fw(for)d Fx(\013)1835 3813 y Fs(0)1835 3866 y(D)p Ft(;\033)1949 3844 y Fw(.)39 b(In)29 b(p)l(articular,)j(one)d(has)739 4031 y Fn(A)805 3997 y Fo(0)805 4051 y Fs(D)883 4031 y Fv(=)22 b(1)-18 b(l)1017 4043 y Fs(2)1072 4031 y Fn(\012)18 b(B)s Fv(\()p Fk(C)1305 3997 y Fs(2)1342 4031 y Fv(\))p Fx(;)99 b Fn(A)1562 3997 y Fo(0)1562 4051 y Fs(D)1639 4031 y Fv(=)23 b Fx(J)1773 4043 y Fs(D)1827 4031 y Fn(A)1893 4043 y Fs(D)1947 4031 y Fx(J)1993 4043 y Fs(D)2047 4031 y Fx(;)99 b Fn(A)2235 4043 y Fs(D)2290 4031 y Fn(j)p Fx(\014)t(;)14 b(D)r Fn(i)23 b Fv(=)g Fn(H)h Fv(=)f Fn(A)2863 3997 y Fo(0)2863 4051 y Fs(D)2917 4031 y Fn(j)p Fx(\014)t(;)14 b(D)r Fn(i)p Fx(;)515 4204 y Fw(and)1141 4303 y Fv(e)1178 4269 y Fo(\000)p Ft(\014)s(L)1317 4277 y Fr(D)1362 4269 y Ft(=)p Fs(2)1433 4303 y Fv(\()p Fx(B)23 b Fn(\012)18 b Fv(1)-18 b(l)1681 4315 y Fs(2)1718 4303 y Fv(\))p Fn(j)p Fx(\014)t(;)14 b Fv(D)p Fn(i)24 b Fv(=)f Fx(J)2114 4315 y Fs(D)2168 4303 y Fv(\()p Fx(B)2267 4269 y Fo(\003)2324 4303 y Fn(\012)18 b Fv(1)-18 b(l)2454 4315 y Fs(2)2490 4303 y Fv(\))p Fn(j)p Fx(\014)t(;)14 b Fv(D)p Fn(i)p Fx(:)515 4461 y Fy(De\034ning,)28 b(on)f Fn(H)d Fv(=)f Fn(H)1236 4473 y Fs(D)1308 4461 y Fn(\012)18 b(F)8 b Fy(,)28 b Fx(J)j Fv(:=)23 b Fx(J)1744 4473 y Fs(D)1816 4461 y Fn(\012)18 b Fx(J)1945 4473 y Fs(F)1992 4461 y Fy(,)28 b(it)g(follo)n(ws)f(that)g(the)h(v)n(ector) 1490 4634 y Fn(j)p Fv(0)p Fn(i)22 b Fv(:=)h Fn(j)p Fx(\014)28 b Fv(=)22 b(2)p Fx(\031)s(=a)p Fn(i)c(\012)g(j)p Fv(0)p Fx(;)c Fv(F)p Fn(i)827 b Fy(\(26\))515 4807 y(is)33 b(a)g(GNS)h (represen)n(tativ)n(e)d(of)j(the)f(KMS)h(state)f(at)g(in)n(v)n(erse)f (temp)r(erature)h Fx(\014)k Fv(=)3162 4774 y Fs(2)p Ft(\031)p 3162 4788 75 4 v 3181 4836 a(a)3280 4807 y Fy(for)515 4907 y(the)31 b(free)f(dynamics)g Fx(\013)1246 4876 y Fs(0)1246 4927 y Ft(\033)1322 4907 y Fy(on)h Fn(A)d Fv(=)g Fn(A)1694 4919 y Fs(D)1769 4907 y Fn(\012)20 b(A)1920 4919 y Fs(F)p Ft(;R)2037 4907 y Fy(.)47 b(This)30 b(suggests)g(to)g (treat)h(the)g(problem)515 5006 y(at)c(hand)h(as)f(one)g(of)g(return)g (to)h(equilibrium.)1905 5255 y(12)p eop end %%Page: 13 13 TeXDict begin 13 12 bop 639 523 a Fy(The)28 b(rest)f(of)g(the)h (argumen)n(t)f(then)h(pro)r(ceeds)f(in)g(three)h(steps:)639 623 y(\(a\))22 b(One)f(pro)n(v)n(es)f(the)i(existence)g(of)f(a)g(GNS)i (represen)n(tativ)n(e)c Fn(j)p Fx(\025)p Fn(i)24 b(2)g(H)q Fy(,)e(de\034ned)g(b)r(elo)n(w,)515 722 y(of)i(the)h(KMS)g(state)f(for) g(the)h(p)r(erturb)r(ed)g(dynamics)f(at)g(the)h(same)f(temp)r(erature)g 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b(essential)t(ly)g(self-adjoint)h(on)f Fx(D)r Fv(\()p Fx(L)2346 2839 y Fs(0)2383 2827 y Fv(\))17 b Fn(\\)h Fx(D)r Fv(\()p Fx(I)7 b Fv(\))18 b Fn(\\)g Fx(D)r Fv(\()p Fx(J)8 b(I)f(J)h Fv(\))30 b Fw(and,)g(for)515 2927 y(al)t(l)h Fx(B)c Fn(2)c(A)p Fw(,)1521 3026 y Fx(\013)1574 2992 y Ft(\025)1574 3047 y(\033)1619 3026 y Fv(\()p Fx(B)t Fv(\))g(=)g(e)1898 2992 y Fs(i)p Ft(L)1963 3001 y Fi(\025)2001 2992 y Ft(\033)2046 3026 y Fx(B)t Fv(e)2150 2992 y Fo(\000)p Fs(i)p Ft(L)2267 3001 y Fi(\025)2305 2992 y Ft(\033)2350 3026 y Fx(:)639 3192 y Fy(A)31 b(useful)f(feature)g(of)g(the)g (standard)f(Liouvillean)g(\(in)i(fact,)f(the)h(motiv)-5 b(ation)29 b(for)h(its)515 3292 y(de\034nition!\))48 b(is)31 b(that)g(the)g(unitary)g(it)g(generates)f(lea)n(v)n(es)f(the)j (equilibrium)f(state)g(of)g(the)515 3392 y(coupled)c(system)g(in)n(v)-5 b(arian)n(t,)27 b(see)g(\(29\))g(b)r(elo)n(w.)515 3558 y Fm(Prop)s(osition)j(3.4)40 b Fw(The)c(ve)l(ctor)e Fn(j)p Fv(0)p Fn(i)g 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Fv(=)e Fn(A)1961 4200 y Fs(D)2034 4188 y Fn(\012)c(A)2183 4200 y Fs(F)p Ft(;R)2330 4188 y Fw(and)30 b(it)g(satis\034es)1757 4370 y Fx(L)1814 4382 y Ft(\025)1857 4370 y Fn(j)p Fx(\025)p Fn(i)24 b Fv(=)f(0)p Fx(:)1094 b Fy(\(29\))639 4569 y Fw(Pr)l(o)l(of.)77 b Fy(T)-7 b(o)27 b(sho)n(w)g(that)h Fn(j)p Fv(0)p Fn(i)23 b(2)g Fv(Dom\(e)1882 4539 y Fo(\000)1944 4517 y Fi(\031)p 1944 4526 36 3 v 1946 4559 a(a)1996 4524 y Fe(e)1990 4539 y Ft(L)2036 4548 y Fi(\025)2079 4569 y Fv(\))28 b Fy(w)n(e)f(c)n(hec)n(k)g(that)g(the)h(Dyson)g(series) 993 4738 y Fj(X)990 4917 y Ft(n)p Fo(\025)p Fs(0)1116 4817 y Fv(\()p Fn(\000)p Fx(\025)p Fv(\))1293 4783 y Ft(n)1353 4704 y Fj(Z)1436 4725 y Ft(\031)r(=a)1399 4893 y Fs(0)1565 4817 y Fv(d)p Fx(t)1641 4829 y Fs(1)1692 4817 y Fn(\001)14 b(\001)g(\001)1803 4704 y Fj(Z)1886 4725 y Ft(t)1911 4733 y Fi(n)p Fg(\000)p Fr(1)1849 4893 y Fs(0)2043 4817 y Fv(d)p Fx(t)2119 4829 y Ft(n)2192 4817 y Fx(\013)2245 4783 y Fs(0)2245 4838 y(i)p Ft(t)2289 4846 y Fi(n)2333 4817 y Fv(\()p Fx(I)7 b Fv(\))14 b Fn(\001)g(\001)g (\001)h Fx(\013)2619 4783 y Fs(0)2619 4838 y(i)p Ft(t)2663 4846 y Fr(1)2699 4817 y Fv(\()p Fx(I)7 b Fv(\))p Fn(j)p Fv(0)p Fn(i)328 b Fy(\(30\))1905 5255 y(13)p eop end %%Page: 14 14 TeXDict begin 14 13 bop 515 523 a Fy(con)n(v)n(erges.)34 b(W)-7 b(e)27 b(write)f(the)i(in)n(teraction)d(op)r(erator)h(con)n(v)n (enien)n(tly)f(as)h Fx(I)k Fv(=)23 b Fx(GQ)p Fv([)p Fx(g)s Fv(])p Fy(,)k(where)515 623 y Fx(G)c Fv(=)g Fx(A)16 b Fv(+)g Fx(A)912 593 y Fo(y)973 623 y Fy(and)26 b Fx(g)s Fv(\()p Fx(x)p Fv(\))e(=)e Fx(a\016)s Fv(\()p Fx(x)1561 593 y Fs(0)1599 623 y Fv(\))p Fx(x)1678 593 y Fs(1)1716 623 y Fx(\032)p Fv(\()p Fx(x)1838 635 y Fo(\003)1877 623 y Fv(\()p Fx(x)p 1909 636 48 4 v 1 w Fv(\)\))27 b Fy(has)f(supp)r(ort)g(in)g Fx(W)2674 635 y Fs(R)2727 623 y Fy(,)h(c.f.)37 b(\(16\).)f(In)26 b(\(30\))515 722 y(w)n(e)h(ha)n(v)n(e)f(set,)i(for)f(real)g Fx(s)p Fy(,)1275 897 y Fx(\013)1328 863 y Fs(0)1328 918 y(i)p Ft(s)1383 897 y Fv(\()p Fx(I)7 b Fv(\))23 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2839 y Fx(L)572 2851 y Fs(F)639 2839 y Fy(has)21 b(absolutely)f(con)n(tin)n(uous)g(sp)r (ectrum)h(co)n(v)n(ering)e(the)j(en)n(tire)e(real)g(axis,)i(and)f(a)g (single)515 2939 y(em)n(b)r(edded)f(eigen)n(v)-5 b(alue)19 b(at)h(the)h(origin.)33 b(This)20 b(eigen)n(v)-5 b(alue)19 b(is)h(simple)g(and)g(has)f(eigen)n(v)n(ector)515 3038 y Fn(j)p Fv(0)p Fx(;)14 b Fv(F)p Fn(i)p Fy(.)42 b(It)29 b(follo)n(ws)g(that)g Fx(L)1372 3050 y Fs(0)1438 3038 y Fy(has)g(absolutely)g(con)n(tin)n(uous)f(sp)r(ectrum)h(co)n(v)n (ering)e(the)j(axis)515 3138 y(and)22 b(three)f(em)n(b)r(edded)i(eigen) n(v)-5 b(alues)20 b(at)i Fv(0)p Fx(;)14 b Fn(\006)p Fx(E)5 b Fy(,)22 b(the)h(one)e(at)h Fv(0)g Fy(b)r(eing)g(doubly)f(degenerate.) 639 3238 y(Our)37 b(goal)f(is)i(to)f(sho)n(w)g(that)h(the)g(nonzero)e (eigen)n(v)-5 b(alues)36 b(are)h(unstable)g(under)h(the)515 3337 y(p)r(erturbation)h Fx(\025)p Fv(\()p Fx(I)34 b Fn(\000)26 b Fx(J)8 b(I)f(J)h Fv(\))p Fy(,)44 b(and)39 b(that)i(the)f(degeneracy)e(of)i(the)g(eigen)n(v)-5 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1 w Fv(\))23 b Fn(3)h Fx(f)31 b Fn(7!)23 b Fx(W)12 b(f)37 b Fy(with)1107 4417 y Fv(\()p Fx(W)12 b(f)d Fv(\)\()p Fk({)s Fx(;)14 b(k)p 1438 4430 46 4 v 1485 4437 a Fo(?)1541 4417 y Fv(\))23 b(:=)1707 4340 y Fj(p)p 1790 4340 352 4 v 77 x Fx(!)1842 4429 y Fo(?)1911 4417 y Fv(cosh)13 b Fk({)2184 4395 y Fj(b)2169 4417 y Fx(f)8 b Fv(\()p Fx(!)2302 4429 y Fo(?)2372 4417 y Fv(sinh)14 b Fk({)s Fx(;)g(k)p 2629 4430 46 4 v 2676 4437 a Fo(?)2732 4417 y Fv(\))p Fx(;)444 b Fy(\(33\))515 4610 y(where)36 b Fx(!)816 4622 y Fo(?)911 4610 y Fv(:=)1037 4540 y Fj(p)p 1120 4540 397 4 v 70 x Fn(j)p Fx(k)p 1143 4623 46 4 v 1189 4631 a Fo(?)1245 4610 y Fn(j)1268 4587 y Fs(2)1324 4610 y Fv(+)18 b Fx(m)1480 4587 y Fs(2)1554 4610 y Fy(and)37 b(where)1990 4589 y Fj(b)1974 4610 y Fx(f)46 b Fy(is)37 b(the)g(F)-7 b(ourier)36 b(transform)g(of)h Fx(f)9 b Fy(.)65 b(The)515 4710 y(adv)-5 b(an)n(tage)33 b(of)i(this)g(represen)n (tation)e(of)i(the)g(Hilb)r(ert)g(space)f(is)h(that)g(the)g(op)r (erator)e Fx(K)6 b Fy(,)515 4810 y(de\034ned)26 b(in)h(\(7\),)g(tak)n (es)f(the)g(particularly)f(simple)i(form)f Fx(K)i Fv(=)23 b(i)p Fx(@)2560 4822 y Fu({)2612 4810 y Fy(.)36 b(The)27 b(transformation)515 4909 y Fx(W)46 b Fy(lifts)35 b(to)f(F)-7 b(o)r(c)n(k)34 b(space)f(in)h(the)h(usual)f(w)n(a)n(y)-7 b(.)55 b(W)-7 b(e)35 b(do)f(not)g(in)n(tro)r(duce)g(new)g(names)g(for) 1905 5255 y(15)p eop end %%Page: 16 16 TeXDict begin 16 15 bop 515 523 a Fy(spaces)26 b(and)g(op)r(erators)f (in)i(the)g(transformed)f(system.)36 b(The)27 b(Liouville)g(op)r (erator)e(\(16\))h(is)774 688 y Fx(L)831 700 y Ft(\025)957 688 y Fv(=)83 b Fx(L)1162 700 y Fs(D)1234 688 y Fv(+)18 b Fx(L)1374 700 y Fs(F)1439 688 y Fv(+)g Fx(\025V)5 b(;)780 813 y(L)837 825 y Fs(0)957 813 y Fv(=)83 b Fx(L)1162 825 y Fs(D)1234 813 y Fv(+)18 b Fx(aL)1418 825 y Fs(F)1464 813 y Fx(;)69 b(L)1613 825 y Fs(D)1690 813 y Fv(=)23 b Fx(H)1847 825 y Fs(D)1919 813 y Fn(\012)18 b Fv(1)-18 b(l)2049 825 y Fs(2)2104 813 y Fn(\000)18 b Fv(1)-18 b(l)2234 825 y Fs(2)2289 813 y Fn(\012)18 b Fx(H)2441 825 y Fs(D)2495 813 y Fx(;)69 b(L)2644 825 y Fs(F)2714 813 y Fv(=)23 b(d\000\(i)p Fx(@)2999 825 y Fu({)3051 813 y Fv(\))p Fx(;)125 b Fy(\(34\))807 959 y Fx(V)102 b Fv(=)83 b Fx(I)25 b Fn(\000)18 b Fx(J)8 b(I)f(J)o(;)97 b(I)30 b Fv(=)23 b Fx(G)18 b Fn(\012)g Fv(1)-18 b(l)1878 971 y Fs(2)1933 959 y Fn(\012)2059 902 y Fx(a)p 2026 939 111 4 v 2026 956 a Fn(p)p 2095 956 42 4 v 69 x Fv(2)2161 891 y Fj(\010)2209 959 y Fx(a)2253 924 y Fo(y)2287 959 y Fv(\()p Fx(g)s Fv(\))19 b(+)f Fx(a)p Fv(\()p Fx(g)s Fv(\))2647 891 y Fj(\011)3231 959 y Fy(\(35\))515 1177 y(acting)k(on)g(the)h(Hilb)r(ert)g(space)f Fn(H)i Fv(=)e Fk(C)1746 1147 y Fs(2)1792 1177 y Fn(\012)8 b Fk(C)1925 1147 y Fs(2)1970 1177 y Fn(\012)g(F)g Fy(,)24 b(where)e Fn(F)31 b Fy(is)22 b(the)h(b)r(osonic)f(F)-7 b(o)r(c)n(k)22 b(space)515 1277 y(o)n(v)n(er)d Fx(L)743 1247 y Fs(2)779 1277 y Fv(\()p Fk(R)871 1247 y Ft(d)910 1277 y Fx(;)14 b Fv(d)p Fk({)k Fv(d)1112 1247 y Ft(d)p Fo(\000)p Fs(1)1236 1277 y Fx(k)p 1236 1290 46 4 v 1281 1298 a Fo(?)1338 1277 y Fv(\))p Fy(.)34 b(In)21 b(\(35\))g Fx(G)g Fy(is)f(the)h Fv(2)5 b Fn(\002)g Fv(2)18 b Fy(matrix)j(with)g Fv(0)f Fy(on)g(the)h(diagonal)e(and)515 1376 y Fv(1)25 b Fy(on)h(the)g (o\033-diagonals,)e(and)i Fx(g)s Fv(\()p Fk({)s Fx(;)14 b(k)p 1671 1389 V 1717 1397 a Fo(?)1773 1376 y Fv(\))24 b(=)1916 1309 y Fj(\000)1954 1376 y Fx(W)12 b Fv(\012)2104 1346 y Fo(\000)p Fs(1)p Ft(=)p Fs(2)2260 1376 y Fx(x)2307 1388 y Fs(1)2345 1376 y Fx(\032)p Fv(\()p Fx(x)2467 1388 y Fo(\003)2506 1376 y Fn(j)2529 1388 y Ft(\034)7 b Fs(=0)2655 1376 y Fv(\))2687 1309 y Fj(\001)2725 1376 y Fv(\()p Fk({)s Fx(;)14 b(k)p 2852 1389 V 2899 1397 a Fo(?)2955 1376 y Fv(\))26 b Fy(is)g(giv)n(en)f(in)515 1488 y(\(17\).)36 b(The)28 b(action)f(of)g Fx(j)1270 1509 y Fr(F)1315 1488 y Fy(,)h(\(25\),)f(is)g(giv)n(en)g(b)n(y)1979 1421 y Fj(\000)2017 1488 y Fx(j)2051 1509 y Fr(F)2096 1488 y Fx(f)2146 1421 y Fj(\001)2183 1488 y Fv(\()p Fk({)s Fx(;)14 b(k)p 2310 1501 V 2357 1509 a Fo(?)2413 1488 y Fv(\))23 b(=)p 2556 1420 50 4 v 23 w Fx(f)9 b Fv(\()p Fn(\000)p Fk({)s Fx(;)14 b(k)p 2798 1501 46 4 v 2844 1509 a Fo(?)2900 1488 y Fv(\))p Fy(.)639 1588 y(W)-7 b(e)28 b(describ)r(e)f(no)n(w)g (the)h(complex)f(deformation.)36 b(Let)28 b Fx(\022)d Fn(2)f Fk(R)p Fy(.)37 b(The)27 b(map)753 1753 y Fx( )807 1765 y Ft(\022)844 1753 y Fv(\()p Fk({)931 1765 y Fs(1)969 1753 y Fx(;)14 b(:)g(:)g(:)g(;)g Fk({)1209 1765 y Ft(n)1254 1753 y Fv(\))24 b(:=)1420 1686 y Fj(\000)1458 1753 y Fx(U)1515 1765 y Ft(\022)1553 1753 y Fx( )1610 1686 y Fj(\001)1648 1753 y Fv(\()p Fk({)1735 1765 y Fs(1)1773 1753 y Fx(;)14 b(:)g(:)g(:)f(;)h Fk({)2012 1765 y Ft(n)2058 1753 y Fv(\))23 b(:=)g(e)2261 1719 y Fs(i)p Ft(\022)r Fs(\()p Fu({)2385 1727 y Fr(1)2416 1719 y Fs(+)p Fo(\001\001\001)o Fu({)2571 1727 y Fi(n)2612 1719 y Fs(\))2642 1753 y Fx( )s Fv(\()p Fk({)2786 1765 y Fs(1)2824 1753 y Fx(;)14 b(:)g(:)g(:)f(;)h Fk({)3063 1765 y Ft(n)3109 1753 y Fv(\))515 1918 y Fy(de\034nes)36 b(a)g(unitary)f(group)h(on)g Fn(F)44 b Fy(\(w)n(e)36 b(are)f(not)h(displa)n(ying)f(the)i(v)-5 b(ariables)35 b Fx(k)p 3020 1931 V 3066 1939 a Fo(?)3158 1918 y Fy(in)i(the)515 2018 y(argumen)n(t)26 b(of)h Fx( )j Fy(since)d Fx(U)1324 2030 y Ft(\022)1389 2018 y Fy(do)r(es)f(not)i(act)e(on)h(them\).)38 b(An)27 b(easy)g(calculation)f(sho)n(ws)g(that)515 2183 y Fx(L)572 2195 y Ft(\025)615 2183 y Fv(\()p Fx(\022)r Fv(\))e(:=)e Fx(U)911 2195 y Ft(\022)949 2183 y Fx(L)1006 2195 y Ft(\025)1049 2183 y Fx(U)1115 2148 y Fo(\003)1106 2203 y Ft(\022)1176 2183 y Fv(=)g Fx(L)1320 2195 y Fs(0)1357 2183 y Fv(\()p Fx(\022)r Fv(\))11 b(+)g Fx(\025V)20 b Fv(\()p Fx(\022)r Fv(\))p Fx(;)63 b(L)1913 2195 y Fs(0)1950 2183 y Fv(\()p Fx(\022)r Fv(\))24 b(=)f Fx(L)2224 2195 y Fs(0)2272 2183 y Fn(\000)11 b Fx(a\022)r(N)t(;)62 b(V)19 b Fv(\()p Fx(\022)r Fv(\))24 b(=)e Fx(I)7 b Fv(\()p Fx(\022)r Fv(\))k Fn(\000)g Fx(J)d(I)f Fv(\()p Fx(\022)r Fv(\))p Fx(J)o(;)3231 2282 y Fy(\(36\))515 2382 y(where)27 b Fx(N)32 b Fv(=)22 b(d\000\(1)-18 b(l\))28 b Fy(is)f(the)h(n)n(um)n(b)r (er)f(op)r(erator)f(on)h Fn(F)36 b Fy(and)1135 2572 y Fx(I)7 b Fv(\()p Fx(\022)r Fv(\))24 b(=)f Fx(G)c Fn(\012)f Fv(1)-18 b(l)1609 2584 y Fs(2)1664 2572 y Fn(\012)1790 2516 y Fx(a)p 1757 2553 111 4 v 1757 2570 a Fn(p)p 1826 2570 42 4 v 68 x Fv(2)1891 2480 y Fj(n)1946 2572 y Fx(a)1990 2538 y Fo(y)2025 2572 y Fv(\(e)2094 2538 y Fs(i)p Ft(\022)r Fu({)2198 2572 y Fx(g)s Fv(\))18 b(+)g Fx(a)p Fv(\(e)2487 2538 y Fs(i)p 2506 2489 34 3 v Ft(\022)r Fu({)2591 2572 y Fx(g)s Fv(\))2666 2480 y Fj(o)2735 2572 y Fx(;)473 b Fy(\(37\))515 2797 y(where)24 b(w)n(e)g(ha)n(v)n(e)g(put)h(the)g (complex)g(conjugate)p 2045 2730 42 4 v 24 w Fx(\022)i Fy(in)e(the)g(argumen)n(t)f(of)g(the)i(annihilation)515 2897 y(op)r(erator)g(in)h(\(37\))h(in)f(view)h(of)f(the)h (complexi\034cation)f(of)g Fx(\022)r Fy(.)515 3049 y Fm(Lemma)k(4.1)41 b Fw(L)l(et)1198 3245 y Fx(\022)1237 3257 y Fs(0)1274 3245 y Fv(\()p Fx(m;)14 b(d)p Fv(\))24 b(:=)1626 3128 y Fj(\032)1758 3192 y Fn(1)111 b Fw(if)31 b Fx(m)23 b Fn(6)p Fv(=)f(0)29 b Fw(and)i Fx(d)23 b Fn(\025)g Fv(1)1739 3263 y Ft(d)p Fo(\000)p Fs(1)p 1739 3277 120 4 v 1783 3324 a(2)1952 3295 y Fw(if)31 b Fx(m)23 b Fv(=)f(0)29 b Fw(and)i Fx(d)23 b Fn(\025)g Fv(2)3231 3245 y Fy(\(38\))515 3457 y Fw(wher)l(e)33 b Fx(m)c Fn(\025)g Fv(0)j Fw(is)h(the)g(mass)g (of)h(the)f(\034eld)h(and)f Fx(d)g Fw(is)h(the)f(sp)l(atial)h (dimension.)49 b(W)-6 b(e)33 b(have)515 3556 y Fv(e)552 3526 y Fs(i)p Ft(\022)r Fu({)655 3556 y Fx(W)12 b Fv(\012)805 3526 y Fo(\000)p Fs(1)p Ft(=)p Fs(2)962 3556 y Fx(h)38 b Fn(2)g Fx(L)1198 3526 y Fs(2)1235 3556 y Fv(\()p Fk(R)1327 3526 y Ft(d)1366 3556 y Fx(;)14 b(d)p Fk({)s Fx(dk)p 1547 3569 46 4 v 1594 3577 a Fo(?)1650 3556 y Fv(\))38 b Fw(for)h(al)t(l)g Fx(\022)i Fn(2)d Fk(C)g Fw(satisfying)i Fn(j)p Fx(\022)r Fn(j)e Fx(<)g(\022)2904 3568 y Fs(0)2979 3556 y Fw(and)h(for)g(al)t(l)515 3656 y Fx(h)28 b Fn(2)h(S)6 b Fv(\()p Fk(R)823 3626 y Ft(d)862 3656 y Fx(;)14 b Fk(C)p Fv(\))p Fw(.)48 b(Mor)l(e)l(over,)35 b(for)e Fn(j)p Fx(\022)r Fn(j)c Fx(<)f(\022)1841 3668 y Fs(0)1878 3656 y Fw(,)34 b Fx(L)1994 3668 y Ft(\025)2037 3656 y Fv(\()p Fx(\022)r Fv(\))g Fw(is)f(a)g(close)l(d)g(op)l(er)l(ator)h(on)f(the)g(dense)515 3756 y(domain)e Fn(D)25 b Fv(=)e(Dom\()p Fx(L)1252 3768 y Fs(0)1289 3756 y Fv(\))c Fn(\\)f Fv(Dom)q(\()p Fx(N)9 b Fv(\))p Fw(.)639 3908 y(Pr)l(o)l(of.)60 b Fx(L)973 3920 y Fs(0)1009 3908 y Fv(\()p Fx(\022)r Fv(\))36 b Fy(is)e(a)h(normal)e(op)r(erator,)i(so)f(it)h(is)f(closed.)57 b(Assume)35 b(w)n(e)f(kno)n(w)g(that)515 4007 y Fv(e)552 3977 y Fs(i)p Ft(\022)r Fu({)655 4007 y Fx(W)12 b Fv(\012)805 3977 y Fo(\000)p Fs(1)p Ft(=)p Fs(2)962 4007 y Fn(S)6 b Fv(\()p Fk(R)1110 3977 y Ft(d)1149 4007 y Fx(;)14 b Fk(C)p Fv(\))23 b Fn(\032)g Fx(L)1446 3977 y Fs(2)1483 4007 y Fv(\()p Fk(R)1575 3977 y Ft(d)1614 4007 y Fx(;)14 b(d)p Fk({)s Fx(dk)p 1795 4020 V 1841 4028 a Fo(?)1898 4007 y Fv(\))p Fy(,)21 b(and)e(recall)f(that)h Fx(x)2558 4019 y Fs(1)2596 4007 y Fx(\032)p Fv(\()p Fx(x)2718 4019 y Fo(\003)2757 4007 y Fn(j)2780 4019 y Ft(\034)7 b Fs(=0)2906 4007 y Fv(\))23 b Fn(2)g(S)6 b Fv(\()p Fk(R)3187 3977 y Ft(d)3227 4007 y Fx(;)14 b Fk(C)p Fv(\))p Fy(.)515 4107 y(Then,)32 b(for)f Fv(Im)p Fx(\022)g Fn(6)p Fv(=)d(0)j Fy(the)h(p)r(erturbation)e Fx(V)19 b Fv(\()p Fx(\022)r Fv(\))32 b Fy(is)f(in\034nitesimally)g(small)g(w.r.t.)47 b Fx(L)3213 4119 y Fs(0)3250 4107 y Fv(\()p Fx(\022)r Fv(\))p Fy(,)515 4207 y(so)27 b Fx(L)674 4219 y Ft(\025)717 4207 y Fv(\()p Fx(\022)r Fv(\))i Fy(is)f(closed)f(b)n(y)g(stabilit)n(y) h(of)g(closedness.)36 b(F)-7 b(or)27 b Fv(Im)q Fx(\022)e Fv(=)f(0)j Fy(the)h(op)r(erator)e Fx(L)3146 4219 y Ft(\025)3189 4207 y Fv(\()p Fx(\022)r Fv(\))j Fy(is)515 4306 y(ev)n(en)e(selfadjoin) n(t.)639 4406 y(Let)h Fx(h)23 b Fn(2)g(S)6 b Fv(\()p Fk(R)1085 4376 y Ft(d)1125 4406 y Fx(;)14 b Fk(C)p Fv(\))p Fy(.)37 b(A)n(ccording)26 b(to)h(\(33\))h(w)n(e)f(ha)n(v)n(e)1243 4582 y Fv(\()p Fx(W)12 b Fv(\012)1425 4548 y Fo(\000)p Fs(1)p Ft(=)p Fs(2)1581 4582 y Fx(h)p Fv(\)\()p Fk({)s Fx(;)i(k)p 1788 4595 V 1835 4603 a Fo(?)1891 4582 y Fv(\))24 b(=)2033 4560 y Fj(b)2034 4582 y Fx(h)p Fv(\()p Fx(!)2166 4594 y Fo(?)2236 4582 y Fv(sinh)14 b Fk({)s Fx(;)g(k)p 2493 4595 V 2539 4603 a Fo(?)2595 4582 y Fv(\))p Fx(:)515 4759 y Fy(Since)730 4737 y Fj(b)731 4759 y Fx(h)23 b Fn(2)h(S)34 b Fy(w)n(e)27 b(ha)n(v)n(e)f(that)i(for)f(an)n(y)g(in)n (teger)g Fx(n)g Fy(there)h(is)f(a)g(constan)n(t)g Fx(C)2853 4771 y Ft(n)2926 4759 y Fy(s.t.)954 4866 y Fj(\014)954 4916 y(\014)954 4966 y(\014)980 4940 y(b)982 4962 y Fx(h)o Fv(\()p Fx(!)1113 4974 y Fo(?)1183 4962 y Fv(sinh)14 b Fk({)s Fx(;)g(k)p 1440 4975 V 1487 4982 a Fo(?)1543 4962 y Fv(\))1575 4866 y Fj(\014)1575 4916 y(\014)1575 4966 y(\014)1626 4962 y Fx(<)2263 4905 y(C)2322 4917 y Ft(n)p 1723 4942 1184 4 v 1723 5027 a Fv(1)k(+)g([)p Fx(m)1962 5003 y Fs(2)2013 5027 y Fv(sinh)2161 4990 y Fs(2)2212 5027 y Fk({)k Fv(+)c Fn(j)p Fx(k)p 2395 5040 46 4 v 2441 5048 a Fo(?)2497 5027 y Fn(j)2520 5003 y Fs(2)2572 5027 y Fv(cosh)2729 4990 y Fs(2)2780 5027 y Fk({)s Fv(])2861 5003 y Ft(n)2917 4962 y Fx(:)1905 5255 y Fy(16)p eop end %%Page: 17 17 TeXDict begin 17 16 bop 515 523 a Fy(F)-7 b(or)27 b Fx(m)c Fv(=)f(0)27 b Fy(w)n(e)h(th)n(us)f(obtain)g(\(using)h(an)f(ob)n(vious)f (c)n(hange)h(of)g(v)-5 b(ariables\))27 b(the)h(estimate)650 639 y Fj(Z)696 827 y Fu(R)756 752 y Fv(d)p Fk({)k Fv(e)926 718 y Fs(2)p Ft(\022)993 692 y Fg(0)1014 718 y Fo(j)p Fu({)s Fo(j)1119 639 y Fj(Z)1166 827 y Fu(R)1208 811 y Fi(d)p Fg(\000)p Fr(1)1334 752 y Fv(d)p Fx(k)p 1380 765 46 4 v 1426 773 a Fo(?)1523 656 y Fj(\014)1523 706 y(\014)1523 756 y(\014)1549 730 y(b)1551 752 y Fx(h)p Fv(\()p Fx(!)1683 764 y Fo(?)1752 752 y Fv(sinh)14 b Fk({)s Fx(;)g(k)p 2009 765 V 2056 773 a Fo(?)2112 752 y Fv(\))2144 656 y Fj(\014)2144 706 y(\014)2144 756 y(\014)2172 677 y Fs(2)2232 752 y Fx(<)2336 731 y Fj(e)2320 752 y Fx(C)2379 764 y Ft(n)2438 639 y Fj(Z)2484 827 y Fu(R)2544 752 y Fv(d)p Fk({)2778 696 y Fv(e)2815 666 y Fs(2)p Ft(\022)2882 640 y Fg(0)2904 666 y Fo(j)p Fu({)s Fo(j)p 2687 733 400 4 v 2687 809 a Fv([cosh)f Fk({)s Fv(])2962 785 y Ft(d)p Fo(\000)p Fs(1)3231 752 y Fy(\(39\))515 966 y(whic)n(h)27 b(is)h(\034nite)g(pro)n(vided)f Fx(\022)1431 935 y Fo(0)1477 966 y Fv(=)c Fn(j)p Fv(I)p Fx(m\022)r Fn(j)h Fx(<)e Fv(\()p Fx(d)d Fn(\000)f Fv(1\))p Fx(=)p Fv(2)p Fy(.)36 b(If)28 b Fx(m)23 b Fn(6)p Fv(=)g(0)k Fy(then)i(the)f(l.h.s.)37 b(of)27 b(\(39\))515 1065 y(is)g(b)r(ounded)h(from)f(ab)r(o)n(v)n(e)g (b)n(y)920 1166 y Fj(Z)966 1354 y Fu(R)1026 1279 y Fv(d)p Fk({)1145 1166 y Fj(Z)1191 1354 y Fu(R)1233 1338 y Fi(d)p Fg(\000)p Fr(1)1359 1279 y Fv(d)p Fx(k)p 1405 1292 46 4 v 1451 1299 a Fo(?)1535 1279 y Fv(e)1572 1244 y Fs(2)p Ft(\022)1639 1219 y Fg(0)1661 1244 y Fo(j)p Fu({)s Fo(j)2310 1222 y Fx(C)2375 1192 y Fs(2)2369 1243 y Ft(n)p 1762 1260 1202 4 v 1762 1344 a Fv([1)p Fx(=)p Fv(2)17 b(+)h Fx(m)2084 1320 y Fs(2)2135 1344 y Fv(sinh)2283 1307 y Fs(2)2334 1344 y Fk({)s Fv(])2415 1320 y Ft(n)2461 1344 y Fv([1)p Fx(=)p Fv(2)f(+)h Fn(j)p Fx(k)p 2733 1357 46 4 v 2779 1365 a Fo(?)2835 1344 y Fn(j)2858 1320 y Fs(2)2895 1344 y Fv(])2918 1320 y Ft(n)515 1501 y Fy(whic)n(h)27 b(is)h(\034nite)g(if)g Fx(\022)1165 1471 y Fo(0)1212 1501 y Fv(=)22 b Fn(j)p Fv(I)p Fx(m\022)r Fn(j)h Fx(<)g(n)p Fy(,)28 b(and)f Fx(n)h Fy(can)f(b)r(e)h(c)n(hosen)e(arbitrarily)g (large.)244 b Fh(\004)515 1730 y Fl(4.2)112 b(Sp)s(ectra)38 b(of)f Fc(L)1373 1745 y Fb(\025)1419 1730 y Fa(\()p Fc(\022)s Fa(\))g Fl(and)i(of)e Fc(L)1990 1745 y Fb(\025)515 1883 y Fy(The)27 b(goal)g(of)g(this)h(section)f(is)h(to)f(pro)n(v)n(e)f(the) i(follo)n(wing)e(result.)515 2035 y Fm(Theorem)31 b(4.2)41 b Fw(Supp)l(ose)e(the)g(F)-6 b(ermi)40 b(Golden)g(R)n(ule)f(Condition)i (\(18\))e(holds.)69 b(Ther)l(e)515 2135 y(is)35 b(a)f Fx(\025)733 2147 y Fs(0)803 2135 y Fx(>)d Fv(0)j Fw(s.t.)52 b(if)36 b Fv(0)31 b Fx(<)g Fn(j)p Fx(\025)p Fn(j)h Fx(<)f(\025)1664 2147 y Fs(0)1736 2135 y Fw(then)k(the)f(sp)l(e)l(ctrum)g(of)h Fx(L)2581 2147 y Ft(\025)2659 2135 y Fw(c)l(onsists)f(of)h(a)g(simple) 515 2235 y(eigenvalue)26 b(at)f(zer)l(o)h(and)f(is)h(pur)l(ely)f (absolutely)h(c)l(ontinuous)f(on)g(the)g(r)l(e)l(al)h(axis)f (otherwise.)639 2386 y Fy(Remark)37 b(that)h(the)h(sp)r(ectrum)e(of)h Fx(L)1840 2398 y Fs(0)1877 2386 y Fv(\()p Fx(\022)r Fv(\))j(=)f Fx(L)2185 2398 y Fs(0)2247 2386 y Fn(\000)25 b Fx(a\022)r(N)47 b Fy(consists)37 b(of)g(the)i Fw(isolate)l(d)515 2486 y(eigenvalues)e Fn(\006)p Fx(E)k Fy(\(simple\))c(and)f Fv(0)g Fy(\(doubly)h(degenerate\),)g(and)f(of)h(the)f(lines)h(of)f (con-)515 2586 y(tin)n(uous)27 b(sp)r(ectrum)h Fn(f)p Fk(R)18 b Fn(\000)g Fv(i)c Fx(an)g Fv(I)p Fx(m\022)r Fn(g)1705 2598 y Ft(n)p Fs(=1)p Ft(;)p Fs(2)p Ft(;:::)1966 2586 y Fy(.)37 b(W)-7 b(e)28 b(no)n(w)g(analyze)e(the)i(b)r(eha)n (viour)f(of)h(the)515 2685 y(eigen)n(v)-5 b(alues)20 b(of)i Fx(L)1084 2697 y Fs(0)1120 2685 y Fv(\()p Fx(\022)r Fv(\))h Fy(under)e(the)h(p)r(erturbation)f Fx(\025V)f Fv(\()p Fx(\022)r Fv(\))p Fy(.)35 b(The)22 b(strategy)e(is)i(to)f(sho)n (w)g(that)515 2785 y(the)26 b(eigen)n(v)-5 b(alues)25 b Fn(\006)p Fx(E)31 b Fy(are)26 b(unstable)g(under)g(the)g(p)r (erturbation,)g(and)g(that)h(the)f(degener-)515 2885 y(acy)g(of)i(the)g(eigen)n(v)-5 b(alue)26 b(zero)h(is)g(lifted.)38 b(Note)27 b(that)h(the)g(k)n(ernel)e(of)i Fx(L)2723 2897 y Ft(\025)2793 2885 y Fy(is)f(non-empt)n(y)g(b)n(y)515 2984 y(construction,)f(see)i(\(29\).)639 3084 y Fw(Pr)l(o)l(of)47 b(of)f(The)l(or)l(em)g(4.2.)89 b Fy(The)45 b(cen)n(tral)f(part)g(of)g (the)h(pro)r(of)f(is)g(the)h(con)n(trol)e(of)515 3183 y(the)36 b(resonances)e(bifurcating)h(out)h(of)g(the)g(eigen)n(v)-5 b(alues)35 b Fn(\006)p Fx(E)40 b Fy(and)c Fv(0)p Fy(,)i(see)d(Lemma)h (4.3.)515 3283 y(A)j(standard)f(analyticit)n(y)g(argumen)n(t)f(then)j (implies)f(Theorem)e(4.2.)70 b(The)39 b(latter)f(can)515 3383 y(b)r(e)h(summarized)g(as)f(follo)n(ws:)59 b(one)39 b(c)n(hec)n(ks)f(that)i(for)e(all)h(complex)g Fx(z)k Fy(with)c Fv(Im)p Fx(z)27 b(>)22 b Fv(0)p Fy(,)515 3482 y Fx(\022)33 b Fn(7!)f(h)p Fx( )p 788 3459 38 3 v 26 x Ft(\022)826 3482 y Fx(;)14 b Fv(\()p Fx(L)952 3494 y Ft(\025)995 3482 y Fv(\()p Fx(\022)r Fv(\))22 b Fn(\000)g Fx(z)t Fv(\))1284 3452 y Fo(\000)p Fs(1)1372 3482 y Fx(\036)1421 3494 y Ft(\022)1459 3482 y Fn(i)33 b Fy(is)g(analytic)e(in)i Fv(0)e Fx(<)g Fn(j)p Fx(\022)r Fn(j)h Fx(<)e(\022)2457 3494 y Fs(0)2495 3482 y Fy(,)k Fv(Im)p Fx(\022)f(>)e Fv(0)p Fy(,)j(and)e(con)n(tin)n(u-)515 3582 y(ous)e(as)h Fv(Im)p Fx(\022)g Fn(#)e Fv(0)p Fy(,)j(for)e(a)h(dense)g(set)g(of)g (deformation)g(analytic)f(v)n(ectors)g Fx( )s Fy(,)i Fx(\036)g Fy(\(tak)n(e)e(e.g.)515 3682 y(\034nite-particle)k(v)n (ectors)f(of)i(F)-7 b(o)r(c)n(k)34 b(space)g(built)h(from)f(test)h (functions)g Fx(f)9 b Fv(\()p Fk({)s Fv(\))36 b Fy(with)f(com-)515 3781 y(pact)g(supp)r(ort\).)59 b(As)35 b(is)g(w)n(ell)g(kno)n(wn,)h (the)f(real)f(eigen)n(v)-5 b(alues)34 b(of)h Fx(L)2708 3793 y Ft(\025)2751 3781 y Fv(\()p Fx(\022)r Fv(\))h Fy(coincide)f(with)515 3881 y(those)25 b(of)g Fx(L)879 3893 y Ft(\025)922 3881 y Fy(,)h(and)g(a)n(w)n(a)n(y)d(from)i(eigen)n (v)-5 b(alues)24 b(the)i(sp)r(ectrum)g(of)f Fx(L)2608 3893 y Ft(\025)2677 3881 y Fy(is)g(purely)g(absolutely)515 3980 y(con)n(tin)n(uous.)639 4080 y(W)-7 b(e)28 b(no)n(w)f(presen)n(t)g (in)h(more)f(detail)g(the)h(resonance)e(theory)-7 b(.)515 4232 y Fm(Lemma)31 b(4.3)41 b Fw(L)l(et)h Fx(\022)1214 4202 y Fo(0)1283 4232 y Fv(=)k(I)p Fx(m\022)i(>)e Fv(0)p Fw(.)76 b(Ther)l(e)44 b(is)e(a)h Fx(\025)2324 4244 y Fs(1)2404 4232 y Fw(\(indep)l(endent)g(of)h Fx(\022)r Fw(\))e(s.t.)77 b(if)515 4332 y Fn(j)p Fx(\025)p Fn(j)24 b Fx(<)g(\025)770 4344 y Fs(1)821 4332 y Fv(min\(1)p Fx(;)14 b(\022)1111 4301 y Fo(0)1135 4332 y Fv(\))30 b Fw(then)g(in)g(the)h(half-plane)h Fn(f)p Fv(I)p Fx(m)o(z)27 b Fn(\025)d(\000)p Fx(\022)2410 4301 y Fo(0)2433 4332 y Fx(=)p Fv(2)p Fn(g)k Fw(the)j(sp)l(e)l(ctrum)e(of)i Fx(L)3230 4344 y Ft(\025)3273 4332 y Fv(\()p Fx(\022)r Fv(\))515 4431 y Fw(c)l(onsists)i(of)g(four)h(eigenvalues)g Fx(")1584 4443 y Fo(\006)1640 4431 y Fv(\()p Fx(\025)p Fv(\))g Fw(and)f Fx(")1989 4443 y Fs(0)2026 4431 y Fv(\()p Fx(\025)p Fv(\))h Fw(and)g Fv(0)e Fw(only)i(\(which)g(do)g(not)f(dep)l (end)515 4531 y(on)d Fx(\022)r Fw(\).)639 4647 y(Mo)l(er)l(over,)i(we)e (have)h Fx(")1383 4659 y Ft(j)1417 4647 y Fv(\()p Fx(\025)p Fv(\))24 b(=)f Fx(e)1680 4659 y Ft(j)1733 4647 y Fn(\000)18 b Fx(\025)1864 4616 y Fs(2)1902 4647 y Fx(")1941 4603 y Fs(\(2\))1941 4670 y Ft(j)2048 4647 y Fv(+)g Fx(o)p Fv(\()p Fx(\025)2251 4616 y Fs(2)2289 4647 y Fv(\))p Fw(,)31 b(wher)l(e)f Fx(j)e Fv(=)23 b(+)p Fx(;)14 b Fn(\000)p Fx(;)g Fv(0)p Fw(,)28 b(and)1364 4841 y Fx(")1403 4798 y Fs(\(2\))1403 4863 y(0)1515 4841 y Fv(=)23 b(i)14 b(Im)g Fx(")1792 4798 y Fs(\(2\))1792 4862 y Fo(\006)1903 4841 y Fv(=)23 b(i)14 b(\(1)k(+)g(e)2240 4807 y Fo(\000)p Fs(2)p Ft(\031)2376 4785 y Fi(E)p 2376 4794 44 3 v 2382 4827 a(a)2434 4841 y Fv(\))p Fx(\030)t(;)702 b Fy(\(40\))515 5006 y Fw(whith)30 b Fx(\030)k Fw(given)d(in)e(\(21\).)1905 5255 y Fy(17)p eop end %%Page: 18 18 TeXDict begin 18 17 bop 515 523 a Fy(W)-7 b(e)28 b(remark)e(that)i(the) g(F)-7 b(ermi)27 b(Golden)h(Rule)f(Condition)h(\(18\))f(asserts)f(that) i Fx(\030)f(>)c Fv(0)p Fy(.)639 623 y Fw(Pr)l(o)l(of)33 b(of)f(L)l(emma)g(4.3.)45 b Fy(By)29 b(an)g(argumen)n(t)g(of)g (stabilit)n(y)g(of)h(the)g(sp)r(ectrum)g(it)g(is)f(not)515 722 y(di\036cult)i(to)f(sho)n(w)g(that)g(the)h(sp)r(ectrum)g(in)f(the)h (indicated)g(half)f(plane)h(consists)e(of)i(four)515 822 y(eigen)n(v)-5 b(alues)26 b(only)-7 b(.)639 922 y(The)27 b(p)r(osition)g(\(at)g(second)f(order)f(in)i Fx(\025)p Fy(\))h(is)e(go)n(v)n(erned)f(b)n(y)h(so-called)g Fw(level)k(shift)g (op)l(er-)515 1021 y(ators)p Fy(,)c(see)f(e.g.)36 b([M2])25 b(and)h(references)e(therein.)36 b(W)-7 b(e)26 b(explain)f(this)h(with) g(the)g(help)f(of)h(the)515 1121 y Fw(F)-6 b(eshb)l(ach)31 b(map)d Fy([BaFS].)639 1220 y(Let)i Fx(e)f Fy(b)r(e)h(an)f(eigen)n(v)-5 b(alue)29 b(of)g Fx(L)1642 1232 y Fs(0)1679 1220 y Fv(\()p Fx(\022)r 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i(the)g Fw(F)-6 b(eshb)l(ach)31 b(map)870 2282 y Fx(F)923 2294 y Ft(e;z)1013 2282 y Fv(\()p Fx(L)1102 2294 y Ft(\025)1145 2282 y Fv(\()p Fx(\022)r Fv(\)\))24 b(:=)f Fx(Q)1483 2294 y Ft(e)1532 2190 y Fj(\020)1582 2282 y Fx(e)18 b Fn(\000)g Fx(\025)1770 2248 y Fs(2)1808 2282 y Fx(V)h Fv(\()p Fx(\022)r Fv(\))p 1980 2215 66 4 v Fx(Q)2046 2302 y Ft(e)2082 2282 y Fv(\()p 2114 2215 57 4 v Fx(L)2170 2229 y Ft(e)2170 2303 y(\025)2214 2282 y Fv(\()p Fx(\022)r Fv(\))g Fn(\000)f Fx(z)t Fv(\))2496 2248 y Fo(\000)p Fs(1)p 2585 2215 66 4 v 2585 2282 a Fx(Q)2651 2302 y Ft(e)2686 2282 y Fx(V)h Fv(\()p Fx(\022)r Fv(\))2858 2190 y Fj(\021)2922 2282 y Fx(Q)2988 2294 y Ft(e)3231 2282 y Fy(\(41\))515 2462 y(is)34 b(w)n(ell)g(de\034ned)h(for)f(all)g Fx(z)j Fn(2)e Fx(B)t Fv(\()p Fx(e;)14 b(\022)1711 2432 y Fo(0)1735 2462 y Fx(=)p Fv(2\))p Fy(.)56 b(This)35 b(map)f(has)g(the)g(follo)n(wing)g(remark)-5 b(able)515 2562 y Fw(isosp)l(e)l(ctr)l(ality)31 b(pr)l(op)l(erty)d Fy([BaFS]:)37 b(for)27 b(all)g Fx(z)g Fn(2)c Fx(B)t Fv(\()p Fx(e;)14 b(\022)2237 2532 y Fo(0)2261 2562 y Fx(=)p Fv(2\))p Fy(,)1158 2717 y Fx(z)26 b Fn(2)d Fv(sp)r(ec\()p Fx(L)1545 2729 y Ft(\025)1589 2717 y Fv(\()p Fx(\022)r Fv(\)\))h Fn(\()-14 b(\))23 b Fx(z)j Fn(2)e Fv(sp)r(ec)2224 2650 y Fj(\000)2262 2717 y Fx(F)2315 2729 y Ft(e;z)2405 2717 y Fv(\()p Fx(L)2494 2729 y Ft(\025)2537 2717 y Fv(\()p Fx(\022)r Fv(\)\))2674 2650 y Fj(\001)2713 2717 y Fx(:)495 b Fy(\(42\))515 2873 y(Th)n(us)24 b(it)h(su\036ces)f(to)g(examine)g (the)h(sp)r(ectrum)f(of)h(the)g(op)r(erator)d Fx(F)2616 2885 y Ft(e;z)2706 2873 y Fv(\()p Fx(L)2795 2885 y Ft(\025)2839 2873 y Fv(\()p Fx(\022)r Fv(\)\))j Fy(whic)n(h)g(acts)515 2972 y(on)e(the)h(\034nite)h(dimensional)e(space)g Fv(Ran)o Fx(Q)1859 2984 y Ft(e)1895 2972 y Fy(.)35 b(W)-7 b(e)24 b(expand)g(the)g(resolv)n(en)n(t)e(in)i(\(41\))f(around)515 3072 y Fx(\025)g Fv(=)g(0)k Fy(and)g(consider)g(sp)r(ectral)g (parameters)f Fx(z)g Fv(=)d Fx(e)18 b Fv(+)g Fx(O)r Fv(\()p Fx(\025)p Fv(\))29 b Fy(to)e(obtain)741 3227 y Fx(F)794 3239 y Ft(e;z)883 3227 y Fv(\()p Fx(L)972 3239 y Ft(\025)1016 3227 y Fv(\()p Fx(\022)r Fv(\)\))d(=)f Fx(Q)1331 3239 y Ft(e)1380 3160 y Fj(\000)1418 3227 y Fx(e)18 b Fn(\000)g Fx(\025)1606 3193 y Fs(2)1644 3227 y Fx(V)g Fv(\()p Fx(\022)r Fv(\))p 1815 3160 V Fx(Q)1882 3247 y Ft(e)1918 3227 y Fv(\()p 1950 3160 57 4 v Fx(L)2006 3239 y Fs(0)2044 3227 y Fv(\()p Fx(\022)r Fv(\))h Fn(\000)f Fx(e)p Fv(\))2322 3193 y Fo(\000)p Fs(1)p 2411 3160 66 4 v 2411 3227 a Fx(Q)2477 3247 y Ft(e)2512 3227 y Fx(V)h Fv(\()p Fx(\022)r Fv(\))2684 3160 y Fj(\001)2737 3227 y Fx(Q)2803 3239 y Ft(e)2857 3227 y Fv(+)f Fx(o)p Fv(\()p Fx(\025)3060 3193 y Fs(2)3098 3227 y Fv(\))p Fx(;)515 3382 y Fy(where)27 b Fv(lim)870 3394 y Ft(\025)p Fo(!)p Fs(0)1027 3382 y Fx(o)p Fv(\()p Fx(\025)1147 3352 y Fs(2)1185 3382 y Fv(\))p Fx(=\025)1307 3352 y Fs(2)1367 3382 y Fv(=)c(0)p Fy(.)37 b(W)-7 b(e)27 b(no)n(w)g(use)h(analyticit)n(y)f(in)g Fx(\022)j Fy(to)e(conclude)f(that)715 3538 y Fx(F)768 3550 y Ft(e;z)858 3538 y Fv(\()p Fx(L)947 3550 y Ft(\025)990 3538 y Fv(\()p Fx(\022)r Fv(\)\))d(=)f Fx(Q)1305 3550 y Ft(e)1354 3470 y Fj(\000)1392 3538 y Fx(e)18 b Fn(\000)g Fx(\025)1580 3503 y Fs(2)1618 3538 y Fx(V)p 1685 3471 V 19 w(Q)1750 3558 y Ft(e)1786 3538 y Fv(\()p 1818 3471 57 4 v Fx(L)1875 3550 y Fs(0)1931 3538 y Fn(\000)g Fx(e)g Fn(\000)g Fv(i0)2219 3550 y Fs(+)2273 3538 y Fv(\))2305 3503 y Fo(\000)p Fs(1)p 2395 3471 66 4 v 2395 3538 a Fx(Q)2460 3558 y Ft(e)2496 3538 y Fx(V)2563 3470 y Fj(\001)2615 3538 y Fx(Q)2681 3550 y Ft(e)2735 3538 y Fv(+)g Fx(o)p Fv(\()p Fx(\025)2938 3503 y Fs(2)2976 3538 y Fv(\))p Fx(;)200 b Fy(\(43\))515 3693 y(where)27 b Fv(i0)820 3705 y Fs(+)902 3693 y Fy(stands)g(for)g(the)h(limit)h(of)e Fv(i)p Fx(")g Fy(as)g Fx(")c Fn(#)g Fv(0)p Fy(.)36 b(The)28 b(op)r(erators)1260 3848 y Fv(\003)1318 3860 y Ft(e)1376 3848 y Fv(:=)23 b Fx(Q)1553 3860 y Ft(e)1588 3848 y Fx(V)p 1655 3782 V 19 w(Q)1720 3869 y Ft(e)1756 3848 y Fv(\()p 1788 3782 57 4 v Fx(L)1845 3860 y 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Fn(\000i)p Fx(;)g Fn(j)p Fv(+)p Fx(;)g Fv(+)p Fn(ig)28 b Fw(of)i Fv(Ran)p Fx(Q)2367 4558 y Fs(0)2434 4546 y Fw(we)g(have)808 4776 y Fv(\003)866 4788 y Fs(0)925 4776 y Fv(=)23 b(i)p Fx(\030)t Fv(e)1113 4742 y Fo(\000)p Ft(\031)1216 4720 y Fi(E)p 1216 4729 44 3 v 1222 4762 a(a)1288 4634 y Fj(")1378 4726 y Fv(e)1415 4695 y Fo(\000)p Ft(\031)1517 4673 y Fi(E)p 1517 4682 V 1523 4715 a(a)1678 4726 y Fn(\000)p Fv(1)1424 4836 y Fn(\000)p Fv(1)128 b(e)1696 4806 y Ft(\031)1746 4784 y Fi(E)p 1746 4793 V 1752 4826 a(a)1846 4634 y Fj(#)1908 4776 y Fx(;)73 b Fw(and)60 b Fv(Im\003)2352 4788 y Fo(\006)p Ft(E)2483 4776 y Fv(=)23 b(\(1)18 b(+)g(e)2783 4742 y Fo(\000)p Fs(2)p Ft(\031)2919 4720 y Fi(E)p 2919 4729 V 2925 4762 a(a)2977 4776 y Fv(\))p Fx(\030)g(;)515 5006 y Fw(wher)l(e)30 b Fx(\030)k Fw(is)c(given)g(in)g(\(21\))1905 5255 y Fy(18)p eop end %%Page: 19 19 TeXDict begin 19 18 bop 515 523 a Fw(R)l(emark.)68 b Fy(The)38 b(Gibbs)h(state)e(of)h(the)h(detector)e(at)h(in)n(v)n(erse)e (temp)r(erature)i 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1501 y Fx(GQ)p Fv([)q Fj(e)-47 b Fx(g)r Fv(])30 b Fy(with)1714 1480 y Fj(e)1698 1501 y Fx(G)c Fv(=)g Fx(A)19 b Fv(+)h Fx(A)2108 1471 y Fo(y)2172 1501 y Fy(and)30 b Fj(e)-47 b Fx(g)s Fv(\()p Fx(x)p Fv(\))27 b(=)e Fx(a\016)s Fv(\()p Fx(x)2769 1471 y Fs(0)2807 1501 y Fv(\))p Fx(x)2886 1471 y Fs(1)2924 1501 y Fx(\032)p Fv(\()p Fx(x)3046 1513 y Fo(\003)3085 1501 y Fv(\()p Fx(x)p Fv(\)\))31 b Fy(has)515 1611 y(supp)r(ort)h(in)h Fx(W)1007 1623 y Fs(R)1060 1611 y Fy(.)52 b(Essen)n(tial)32 b(selfadjoin)n(tness)g(of)2150 1590 y Fj(e)2143 1611 y Fx(L)2200 1623 y Ft(\025)2276 1611 y Fy(can)g(easily)g(b)r(e)h(sho)n(wn)e(using)i(the)515 1710 y(Glimm\025Ja\033e\025Nelson)26 b(comm)n(utator)g(theorem,)h(see)h (e.g.)36 b([FM],)28 b(Section)g(3.)639 1810 y(The)g(Araki-Dyson)e (series)g(expansion)h(giv)n(es)f(\(w)n(eakly)h(on)g(a)g(dense)h(set\)) 556 2059 y Fv(e)593 2025 y Fs(i)p Ft(t)643 2010 y Fe(e)637 2025 y Ft(L)683 2034 y Fi(\025)726 2059 y Fx(M)9 b Fv(e)853 2025 y Fo(\000)p Fs(i)p Ft(t)955 2010 y Fe(e)949 2025 y Ft(L)995 2034 y Fi(\025)1120 2059 y Fv(=)1297 1955 y Fo(1)1270 1980 y Fj(X)1267 2156 y Ft(n)p Fs(=0)1406 2059 y Fx(\025)1454 2025 y Ft(n)1514 1946 y Fj(Z)1597 1967 y Ft(t)1560 2135 y Fs(0)1640 2059 y Fv(d)p Fx(t)1716 2071 y Fs(1)1767 1946 y Fj(Z)1850 1967 y Ft(t)1813 2135 y(t)1838 2143 y Fr(1)1893 2059 y Fv(d)p Fx(t)1969 2071 y Fs(2)2020 2059 y Fn(\001)14 b(\001)g(\001)2131 1946 y Fj(Z)2214 1967 y Ft(t)2177 2135 y(t)2202 2143 y Fi(n)p Fg(\000)p Fr(1)2334 2059 y Fv(d)p Fx(t)2410 2071 y Ft(n)2455 1967 y Fj(h)2511 2038 y(e)2495 2059 y Fx(G)p Fv(\()p Fx(t)2622 2071 y Fs(1)2659 2059 y Fv(\))p Fx(Q)p Fv([)q Fj(e)-47 b Fx(g)21 b Fn(\016)d Fx(B)2964 2071 y Fo(\000)p Ft(at)3077 2079 y Fr(1)3114 2059 y Fv(])p Fx(;)3174 1967 y Fj(h)3227 2059 y Fn(\001)c(\001)g(\001)1267 2293 y(\001)g(\001)g (\001)1378 2201 y Fj(h)1434 2272 y(e)1417 2293 y Fx(G)p Fv(\()p Fx(t)1544 2305 y Ft(n)1590 2293 y Fv(\))p Fx(Q)p Fv([)q Fj(e)-47 b Fx(g)21 b Fn(\016)d Fx(B)1895 2305 y Fo(\000)p Ft(at)2008 2313 y Fi(n)2053 2293 y Fv(])p Fx(;)c Fv(e)2150 2259 y Fs(i)p Ft(tL)2240 2267 y Fr(0)2276 2293 y Fx(M)9 b Fv(e)2403 2259 y Fo(\000)p Fs(i)p Ft(tL)2545 2267 y Fr(0)2580 2201 y Fj(i)2633 2293 y Fn(\001)14 b(\001)g(\001)2744 2201 y Fj(ii)2822 2293 y Fx(;)386 b Fy(\(44\))515 2519 y(where)35 b(w)n(e)g(set)1047 2498 y Fj(e)1031 2519 y Fx(G)p Fv(\()p Fx(t)p Fv(\))i(=)f(e)1365 2489 y Fs(i)p Ft(tL)1455 2497 y Fr(D)1504 2519 y Fx(G)p Fv(e)1606 2489 y Fo(\000)p Fs(i)p Ft(tL)1748 2497 y Fr(D)1797 2519 y Fy(.)61 b(F)-7 b(or)35 b Fx(M)45 b Fn(2)37 b(A)f Fy(an)n(y)f(elemen)n (t)g Fx(M)2927 2489 y Fo(0)2987 2519 y Fn(2)i(A)3145 2489 y Fo(0)3204 2519 y Fy(com-)515 2635 y(m)n(utes)23 b(term)n(wise)f(with)i(the)f(series)f(\(44\),)h(hence)g Fx(M)2148 2605 y Fo(0)2171 2635 y Fv(e)2208 2605 y Fs(i)p Ft(t)2258 2590 y Fe(e)2252 2605 y Ft(L)2298 2614 y Fi(\025)2341 2635 y Fx(M)9 b Fv(e)2468 2605 y Fo(\000)p Fs(i)p Ft(t)2570 2590 y Fe(e)2564 2605 y Ft(L)2610 2614 y Fi(\025)2675 2635 y Fv(=)23 b(e)2800 2605 y Fs(i)p Ft(t)2850 2590 y Fe(e)2844 2605 y Ft(L)2890 2614 y Fi(\025)2932 2635 y Fx(M)9 b Fv(e)3059 2605 y Fo(\000)p Fs(i)p Ft(t)3161 2590 y Fe(e)3155 2605 y Ft(L)3201 2614 y Fi(\025)3243 2635 y Fx(M)3333 2605 y Fo(0)3356 2635 y Fy(.)515 2751 y(Therefore)26 b(w)n(e)h(ha)n(v)n(e)g Fv(e)1242 2721 y Fs(i)p Ft(t)1292 2706 y Fe(e)1286 2721 y Ft(L)1332 2730 y Fi(\025)1374 2751 y Fn(A)p Fv(e)1477 2721 y Fo(\000)p Fs(i)p Ft(t)1579 2706 y Fe(e)1573 2721 y Ft(L)1619 2730 y Fi(\025)1685 2751 y Fn(2)c(A)p Fy(.)1462 b Fh(\004)639 2851 y Fw(Pr)l(o)l(of)34 b(of)f(L)l(emma)g(3.3.)80 b Fy(Essen)n(tial)30 b(selfadjoin)n(tness)g(is)h(sho)n(wn)f(using)g(the)h (Glimm\025)515 2950 y(Ja\033e\025Nelson)26 b(comm)n(utator)g(theorem,)h (see)g(e.g.)36 b([FM])28 b(Section)f(3.1.)36 b(The)28 b(fact)f(that)3286 2929 y Fj(e)3279 2950 y Fx(L)3336 2962 y Ft(\025)515 3060 y Fy(and)g Fx(L)733 3072 y Ft(\025)803 3060 y Fy(de\034ne)g(the)h(same)e(dynamics)h(on)g Fn(A)g Fy(is)g(easily)f(deriv)n(ed)g(b)n(y)h(using)g(that)g Fx(L)3136 3072 y Ft(\025)3197 3060 y Fn(\000)3286 3039 y Fj(e)3279 3060 y Fx(L)3336 3072 y Ft(\025)515 3160 y Fy(b)r(elongs)20 b(to)h(the)g(comm)n(utan)n(t)g(of)g Fn(A)g Fy(\(and)h(e.g.)34 b(applying)20 b(the)i(T)-7 b(rotter)20 b(pro)r(duct)h(form)n(ula\),)515 3260 y(see)27 b(also)f([FM)q(].)2299 b Fh(\004)515 3534 y Fz(References)515 3716 y Fy([BaFS])89 b(V.)32 b(Bac)n(h,)g(J.)f(F)-7 b(r\366hlic)n(h,)32 b(I.)g(Sigal,)g Fw(R)l(eturn)f(to)j(e)l(quilibrium)p Fy(,)f(J.)e(Math.)h(Ph)n(ys.,)851 3816 y Fm(41)p Fy(,)c(no.)f(6,)g (3985-4060)c(\(2000\).)515 3982 y([BiWi])100 b(J.)25 b(Bisognano,)e(E.)i(Wic)n(hmann,)g Fw(On)h(the)h(duality)h(c)l (ondition)g(for)f(a)h(Hermitian)851 4081 y(sc)l(alar)j(\034eld)p Fy(,)d(J.)g(Math.)f(Ph)n(ys.,)h Fm(16)p Fy(,)f(985-1007)d(\(1975\).)515 4247 y([Da])185 b(E.B.)36 b(Da)n(vies,)h Fw(Markovian)i(master)e(e)l (quations)p Fy(,)g(Comm.)f(Math.)f(Ph)n(ys.,)i Fm(39)p Fy(,)851 4347 y(91-110)25 b(\(1974\))515 4513 y([DJ])184 b(J.)36 b(Derezi\253ski,)h(V.)g(Jak)l(\010)-37 b(si\242,)35 b Fw(R)l(eturn)h(to)h(Equilibrium)i(for)f(Pauli-Fierz)g(Sys-)851 4613 y(tems)p Fy(,)28 b(Ann.)g(Henri)f(P)n(oincar\351,)g Fm(4)p Fy(,)g(no.)g(4,)h(739\025793)c(\(2003\).)515 4779 y([DJP])128 b(J.)47 b(Derezi\253ski,)j(V.)d(Jak)l(\010)-37 b(si\242,C.-A.)44 b(Pillet,)52 b Fw(Perturb)l(ation)c(the)l(ory)f(for)h Fx(W)3311 4748 y Fo(\003)3349 4779 y Fw(-)851 4878 y(dynamics,)d (Liouvil)t(le)l(ans)c(and)g(KMS-states)p Fy(,)f(Rev.)f(Math.)g(Ph)n (ys.,)i Fm(15)p Fy(,)g(no.)851 4978 y(5,)28 b(447\025489)c(\(2003\).) 1905 5255 y(19)p eop end %%Page: 20 20 TeXDict begin 20 19 bop 515 523 a Fy([FM])160 b(J.)19 b(F)-7 b(r\366hlic)n(h,)20 b(M.)g(Merkli,)g Fw(The)l(ormal)k (Ionization)p Fy(,)e(Math.)d(Ph)n(ys.)g(Anal.)g(Geom.,)851 623 y Fm(7)p Fy(,)28 b(no.)f(3,)g(239\025287)e(\(2004\))515 789 y([F)-7 b(u])197 b(S.)33 b(F)-7 b(ulling,)33 b Fw(Nonuniqueness)g (of)i(c)l(anonic)l(al)g(\034eld)f(quantization)g(in)g(R)n(ieman-)851 888 y(nian)c(sp)l(ac)l(e-time)p Fy(,)e(Ph)n(ys.)g(Rev.)g(D)g Fm(7)p Fy(,)f(2850-2862)c(\(1973\).)515 1054 y([F)-7 b(uU])135 b(S.)34 b(A.)f(F)-7 b(ulling)33 b(and)g(W.)g(G.)g(Unruh,)i Fw(Comment)f(on)h("Boundary)h(c)l(onditions)851 1154 y(in)30 b(the)g(Unruh)f(pr)l(oblem")p Fy(,)g(Ph)n(ysical)e(Review)h(D)g Fm(70)p Fy(,)f(048701)e(\(2004\).)515 1320 y([JP1])149 b(V.)32 b(Jak)l(\010)-37 b(si\242,)29 b(C.-A.)i(Pillet,)i Fw(On)f(a)h(mo)l(del)h(for)f(quantum)f(friction.)i(II.)f(F)-6 b(ermi's)851 1420 y(golden)24 b(rule)f(and)g(dynamics)i(at)d(p)l (ositive)j(temp)l(er)l(atur)l(e)p Fy(,)c(Comm.)f(Math.)g(Ph)n(ys.,)851 1519 y Fm(176)p Fy(,)27 b(no.)h(3,)f(619\025644)d(\(1996\).)515 1685 y([JP2])149 b(V.)26 b(Jak)l(\010)-37 b(si\242,)24 b(C.-A.)i(Pillet,)h Fw(On)g(a)h(Mo)l(del)h(for)g(Quantum)d(F)-6 b(riction)28 b(III.)h(Er)l(go)l(dic)851 1785 y(Pr)l(op)l(erties)43 b(of)f(the)f(Spin-Boson)h(System)p Fy(,)h(Comm)n(un.)d(Math.)g(Ph)n (ys.,)k Fm(178)p Fy(,)851 1885 y(627-651,)25 b(\(1996\).)515 2051 y([KF)n(GV])46 b(A.)34 b(K)n(ossak)n(o)n(wski,)d(A.)j(F)-7 b(rigerio,)33 b(V.)h(Gorini,)g(M.)g(V)-7 b(erri,)34 b Fw(Quantum)f(Detaile)l(d)851 2150 y(Balanc)l(e)50 b(and)e(KMS)g (Condition)p Fy(,)55 b(Comm)n(un.)47 b(Math.)h(Ph)n(ys.,)53 b Fm(57)p Fy(,)f(97-110)851 2250 y(\(1977\))515 2416 y([M1])172 b(M.)32 b(Merkli,)h Fw(Positive)i(Commutators)f(in)f (Non-Equilibrium)i(Quantum)d(Sta-)851 2516 y(tistic)l(al)f(Me)l (chanics)p Fy(,)e(Comm)n(un.)e(Math.)h(Ph)n(ys.,)g Fm(223)p Fy(,)f(327-362)d(\(2001\).)515 2682 y([M2])172 b(M.)27 b(Merkli,)g Fw(L)l(evel)i(shift)h(op)l(er)l(ators)g(for)f(op)l(en)h (quantum)d(systems)p Fy(.)g(T)-7 b(o)26 b(app)r(ear)851 2781 y(in)i(Journ.)f(Math.)h(Anal.)f(Appl.)515 2947 y([Pi])211 b(C.)28 b(A.)g(Pillet,)h Fw(Quantum)f(dynamic)l(al)j(systems)p Fy(,)c(to)h(app)r(ear.)515 3113 y([Ri])206 b(W.)40 b(Rindler,)i Fw(Essential)f(r)l(elativity)p Fy(,)j(T)-7 b(exts)39 b(and)g(Monographs)e(in)i(Ph)n(ysics,)851 3213 y(Springer)27 b(V)-7 b(erlag)26 b(\(1977\).)515 3379 y([Se])207 b(G.)30 b(Sew)n(ell,)f Fw(Quantum)g(\034elds)j(on)f(manifolds:)43 b(PCT)32 b(and)g(gr)l(avitational)t(ly)h(in-)851 3479 y(duc)l(e)l(d)d(thermal)h(states)p Fy(,)c(Ann.)h(Ph)n(ys.,)g Fm(141)p Fy(,)f(201-224)d(\(1982\).)515 3645 y([T)-7 b(a])195 b(S.)33 b(T)-7 b(ak)i(agi,)32 b Fw(V)-6 b(acuum)33 b(noise)i(and)g(str)l(ess)e(induc)l(e)l(d)i(by)f(uniform)h(ac)l(c)l (eler)l(ation)p Fy(,)851 3744 y(Progress)26 b(of)h(Theoretical)g(Ph)n (ysics,)g Fm(88)p Fy(,)g(1-142)e(\(1986\).)515 3910 y([U])228 b(W.)24 b(Unruh,)g Fw(Notes)h(on)g(black)h(hole)h(evap)l(or)l(ation)p Fy(,)e(Ph)n(ys.)e(Rev.)g(D.)g Fm(14)p Fy(,)g(870-892)851 4010 y(\(1976\).)515 4176 y([UW])143 b(W.)28 b(Unruh,)g(R.)g(W)-7 b(ald,)27 b Fw(What)j(happ)l(ens)h(when)f(an)g(ac)l(c)l(eler)l(ating)g (observer)h(de-)851 4276 y(te)l(cts)e(a)h(R)n(ind)t(ler)h(p)l(article)p Fy(,)e(Ph)n(ys.)e(Rev.)h(D,)g Fm(29)p Fy(,)f(1047-1056)c(\(1984\).)515 4442 y([W)-7 b(a])170 b(R.M.)31 b(W)-7 b(ald,)32 b Fw(Quantum)e (\034eld)j(the)l(ory)g(in)g(curve)l(d)f(sp)l(ac)l(etime)h(and)g(black)h (hole)851 4541 y(thermo)l(dynamics)p Fy(,)d(Univ)n(ersit)n(y)d(of)h (Chicago)f(Press,)h(Chicago)f(Lecture)g(Notes)851 4641 y(in)g(Ph)n(ysics)f(\(1994\).)1905 5255 y(20)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF ---------------0604110849653--