Content-Type: multipart/mixed; boundary="-------------0611090350658" This is a multi-part message in MIME format. ---------------0611090350658 Content-Type: text/plain; name="06-323.keywords" Content-Transfer-Encoding: 7bit Content-Disposition: attachment; filename="06-323.keywords" mean-field limit, quantization, many-body theory, nonlinear Schr dinger equation ---------------0611090350658 Content-Type: application/postscript; name="atomism.ps" Content-Transfer-Encoding: 7bit Content-Disposition: inline; filename="atomism.ps" %!PS-Adobe-2.0 %%Creator: dvips(k) 5.95a Copyright 2005 Radical Eye Software %%Title: atomism.dvi %%Pages: 15 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: CMR17 CMR12 CMR10 CMBX10 CMR6 CMR9 CMBX12 CMR8 CMTI10 %%+ CMSY10 CMMI10 CMMI8 CMSY8 CMEX10 rsfs10 TeX-cmex8 MSBM7 MSBM10 CMMI6 %%+ CMSY6 CMMI9 CMSY9 CMCSC10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips atomism.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2006.11.09:1043 %%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: psfrag.pro 0 0 %% %% This is file `psfrag.pro', %% generated with the docstrip utility. %% %% The original source files were: %% %% psfrag.dtx (with options: `filepro') %% %% Copyright (c) 1996 Craig Barratt, Michael C. 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMCSC10 %!PS-AdobeFont-1.1: CMCSC10 1.0 %%CreationDate: 1991 Aug 18 17:46:49 % Copyright (C) 1997 American Mathematical Society. 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cleartomark %%EndFont %%BeginFont: CMSY9 %!PS-AdobeFont-1.1: CMSY9 1.0 %%CreationDate: 1991 Aug 15 07:22:27 % 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 (CMSY9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY9 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 33 /arrowright put dup 50 /element put dup 55 /mapsto put readonly def /FontBBox{-30 -958 1146 777}readonly 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. All Rights Reserved) readonly def /FullName (CMMI9) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI9 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 32 /psi put dup 76 /L put readonly def /FontBBox{-29 -250 1075 750}readonly def currentdict end currentfile eexec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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 0 /minus put dup 20 /lessequal put readonly def /FontBBox{-4 -948 1329 786}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % 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 (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 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 82 /R put dup 126 /planckover2pi1 put readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec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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 23 /nu put dup 59 /comma put dup 78 /N put dup 107 /k put dup 110 /n put dup 112 /p put dup 116 /t put readonly def /FontBBox{11 -250 1241 750}readonly 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 82 /R put dup 126 /planckover2pi1 put readonly def /FontBBox{0 -504 2615 1004}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: TeX-cmex8 %!PS-AdobeFont-1.0: TeX-cmex8 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\040cmex8) def /FullName (TeX\040cmex8\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-cmex8 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 98 /b put dup 99 /c put readonly def /FontBBox {-29 -2957 1554 772} readonly def currentdict end currentfile eexec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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 10 /angbracketleftbig put dup 11 /angbracketrightbig put dup 12 /vextendsingle put dup 13 /vextenddouble put dup 16 /parenleftBig put dup 17 /parenrightBig put dup 18 /parenleftbigg put dup 19 /parenrightbigg put dup 20 /bracketleftbigg put dup 21 /bracketrightbigg put dup 77 /circleplusdisplay put dup 82 /integraltext put dup 88 /summationdisplay put dup 89 /productdisplay put dup 90 /integraldisplay put dup 98 /hatwide put dup 99 /hatwider put dup 104 /bracketleftBig put dup 105 /bracketrightBig put dup 110 /braceleftBig put dup 111 /bracerightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % 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 (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 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 18 /theta put dup 23 /nu put dup 59 /comma put dup 60 /less put dup 61 /slash put dup 66 /B put dup 69 /E put dup 72 /H put dup 77 /M put dup 78 /N put dup 80 /P put dup 84 /T put dup 102 /f put dup 104 /h put dup 105 /i put dup 106 /j put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 112 /p put dup 113 /q put dup 115 /s put dup 116 /t put dup 120 /x put dup 121 /y put readonly def /FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % 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 (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 14 /delta put dup 18 /theta put dup 22 /mu put dup 23 /nu put dup 25 /pi put dup 26 /rho put dup 28 /tau put dup 30 /phi put dup 32 /psi put dup 34 /epsilon put dup 39 /phi1 put dup 42 /arrowrighttophalf 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 69 /E put dup 70 /F put dup 71 /G put dup 72 /H 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 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 97 /a put dup 98 /b 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 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q 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 readonly def /FontBBox{-32 -250 1048 750}readonly def currentdict end currentfile eexec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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 3 /asteriskmath put dup 10 /circlemultiply put dup 14 /openbullet put dup 20 /lessequal put dup 21 /greaterequal put dup 24 /similar put dup 32 /arrowleft put dup 33 /arrowright put dup 34 /arrowup put dup 35 /arrowdown put dup 38 /arrowsoutheast put dup 39 /similarequal put dup 49 /infinity put dup 50 /element put dup 55 /mapsto put dup 65 /A put dup 70 /F put dup 71 /G put dup 72 /H put dup 95 /logicalor 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 dup 114 /nabla put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052F09F9C8ADE9D907C058B87E9B6964 7D53359E51216774A4EAA1E2B58EC3176BD1184A633B951372B4198D4E8C5EF4 A213ACB58AA0A658908035BF2ED8531779838A960DFE2B27EA49C37156989C85 E21B3ABF72E39A89232CD9F4237FC80C9E64E8425AA3BEF7DED60B122A52922A 221A37D9A807DD01161779DDE7D31FF2B87F97C73D63EECDDA4C49501773468A 27D1663E0B62F461F6E40A5D6676D1D12B51E641C1D4E8E2771864FC104F8CBF 5B78EC1D88228725F1C453A678F58A7E1B7BD7CA700717D288EB8DA1F57C4F09 0ABF1D42C5DDD0C384C7E22F8F8047BE1D4C1CC8E33368FB1AC82B4E96146730 DE3302B2E6B819CB6AE455B1AF3187FFE8071AA57EF8A6616B9CB7941D44EC7A 71A7BB3DF755178D7D2E4BB69859EFA4BBC30BD6BB1531133FD4D9438FF99F09 4ECC068A324D75B5F696B8688EEB2F17E5ED34CCD6D047A4E3806D000C199D7C 515DB70A8D4F6146FE068DC1E5DE8BC57036519F4E72E76E041E60DC739B2906 AFA7A06FE903D993C8FC4DCB46E5D1FF37F627803666E55BC04CF88F13AFAE5C 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMTI10 %!PS-AdobeFont-1.1: CMTI10 1.00B %%CreationDate: 1992 Feb 19 19:56:16 % 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 (CMTI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMTI10 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 /fi put dup 34 /quotedblright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 58 /colon 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 72 /H put dup 73 /I 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 82 /R put dup 83 /S put dup 84 /T put dup 86 /V put dup 87 /W put dup 92 /quotedblleft put dup 97 /a put dup 98 /b 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 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def /FontBBox{-163 -250 1146 969}readonly def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR8 %!PS-AdobeFont-1.1: CMR8 1.0 %%CreationDate: 1991 Aug 20 16:39:40 % 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 (CMR8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR8 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 1 /Delta put dup 6 /Sigma put dup 11 /ff put dup 35 /numbersign put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 61 /equal put dup 72 /H put dup 86 /V put dup 87 /W put dup 99 /c put dup 101 /e put dup 104 /h put dup 105 /i put dup 108 /l put dup 109 /m put dup 110 /n put dup 113 /q put dup 115 /s put dup 116 /t put dup 117 /u put readonly def /FontBBox{-36 -250 1070 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % 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 (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 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 44 /comma put dup 45 /hyphen put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 65 /A put dup 66 /B put dup 67 /C put dup 69 /E put dup 70 /F put dup 71 /G put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 81 /Q put dup 82 /R put dup 84 /T 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 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 121 /y put dup 122 /z put readonly def /FontBBox{-53 -251 1139 750}readonly def 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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 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 49 /one put dup 61 /equal put dup 65 /A put dup 68 /D put dup 70 /F put dup 72 /H put dup 74 /J put dup 75 /K put dup 80 /P put dup 97 /a put dup 98 /b 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 107 /k 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 116 /t put dup 117 /u put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 127 /dieresis put readonly def 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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 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 115 /s put readonly def /FontBBox{-20 -250 1193 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF4E9D2405B169CD5365D6ECED5D768D66D6C 68618B8C482B341F8CA38E9BB9BAFCFAAD9C2F3FD033B62690986ED43D9C9361 3645B82392D5CAE11A7CB49D7E2E82DCD485CBA17D1AFFF95F4224CF7ECEE45C BFB7C8C77C22A01C345078D28D3ECBF804CDC2FE5025FA0D05CCC5EFC0C4F87E CBED13DDDF8F34E404F471C6DD2E43331D73E89BBC71E7BF889F6293793FEF5A C9DD3792F032E37A364C70914843F7AA314413D022AE3238730B420A7E9D0CF5 D0E24F501451F9CDECE10AF7E14FF15C4F12F3FCA47DD9CD3C7AEA8D1551017D 23131C09ED104C052054520268A4FA3C6338BA6CF14C3DE3BAF2EA35296EE3D8 D6496277E11DFF6076FE64C8A8C3419FA774473D63223FFA41CBAE609C3D976B 93DFB4079ADC7C4EF07303F93808DDA9F651F61BCCF79555059A44CBAF84A711 6D98083CEF58230D54AD486C74C4A257FC703ACF918219D0A597A5F680B606E4 EF94ADF8BF91A5096A806DB64EC96636A98397D22A74932EB7346A9C4B5EE953 CB3C80AA634BFC28AA938C704BDA8DC4D13551CCFE2B2784BE8BF54502EBA9AF D49B79237B9C56310550BC30E9108BB06EAC755D6AA4E688EFE2A0AAB17F20FE 00CD0BFF1B9CB6BDA0FA3A29A3117388B6686657A150CE6421FD5D420F4F7FB5 B0DAA1BA19D638676E9CF159AC7325EF17B9F74E082BEF75E10A31C7011C0FFA 99B797CE549B5C45238DD0FADD6B99D233AC69282DF0D91EA2DBD08CE0083904 A6D968D5AE3BD159D01BDFF42D16111BC0A517C66B43972080D9DD4F3B9AE7FB 11B035CE715C1218B2D779761D8D7E9DEBE277531BD58F313EBD27E33BEF9DC5 50C7821A8BBC3B9FDF899D7EAA0B94493B97AFEAC503EB5ED7A7AB6D9A929A8D D186043A1A15F89EDE60FC17A136907ED2A1F8A538DFABC863DA3AE06FE15AA6 C0957AB448B27734124D849C08EDF1FB565B0F939B3062EFA13AD657F147671C F05A2BECC69DD1FA903D10945AC93C49E001031A2824A6542DA4412F8D0829D3 D1F8F66FA8370E0D97EBD9D91CFA51E322EB5C7172F81FE7F7CD1D917A8366AD 83779ABF0BD9EC621E258C2705B46123F7EF26500A6A9056DF27ED58080D5E88 DF972A7A140C6603C293DCBBAD2B14ECC943158A9A2D8E96207775CF61184FF4 C5D3E49CAD9FB4F596D85D528DD5FB878F9D16F65A32DFBCC797E8733920D73F EA5987223E2C8EFB75F928FEBB01745492673ACC89C75BF2717EAFBAD4420AB1 C9EC142942B73D33F2D3F1C9E90A56FF86BE4A64D38CE768238786F6440D2ED5 33BC494ED233EBB6ED2BEC18529E84A72D91A7BE19FE6BFD136F43AA6834D610 CE3171F0521B34BEFF4435E6548B48E8A119BF45CD7518D8DCF80C424AF525A6 FB25F4490FEF92774C162ADB926EC8A731034AC1B71F7FF7CBD71A00F185438C 935AB9CB5EF5DFFD2EFDF7C0E7607369F4FE725F1958C18D0A793984BF105B85 FF43183EB1B29ACE66227A6CBC58E660D5FB0062E5FB019623073FCF406A617D 8EC41458913C5353928A18254EC05B740A44922361839C6FE38BD883F0577C21 B475621B5953A592DC305DB5EAB512B5A5B6AF4021A9A81AD0EF06470F333EA8 C9FC17D6E441A7CDEC628FE8E32C16181875339C6D707CF458B013146ED1BE04 3AD746D9982182ADC46BD4EBB78F98C1B2FBD9547EE65D278AD77AF615653CFD 0A5B0533ACEC6C153C8BF81DAD2F18B14BB18D13D07D4D0D9BED0724B809A063 CA6DD6F9243F6CBE3E59886FDDFA10F4CADCFD787DE3D451E62808C783F3480B 68D4176144C49A86C279582F5A534DD19878EC2E853D5E1677349F3317B33D4D 722E1E2F62EA7F05C57B1A36E53C2D9ECBF4BC19D7066999AFAC5F50F0D1A8E4 A49B654E73459D81F6CCCE38419415E5DB41C23854FF1EE9FACB987FFB7573E4 46DB54C7D80E46B44F18DF7753C11437BBFB7A1311651B135B025765208FA7A7 EAC64FB724F85315AD3CC025711965DB1E6ADC801A4576B69F21FC5BFE0D55D3 10C90C153C7C602A1BCD55DD60380DB1437B1BF77C7D90A576531D3E33542A7C 8B23BC957CF243FDAF6CA41ACB83DA504C6552B78F3DDE31DA8D4C466C241471 25B26362A13025DE5589C8333F76D6F42AAFC2B98FDF7C8A48AC1BD2C5894E66 41548CF962C6342312897D1752C3EE58BB71F25E5F8A52CB1FF9B35FB34B73BE 7F2D3AC0B103E0053C0C6B22B72452CEB0896A77F31753D73CD017B81D00E7E7 FAF107DB20F192195627376A5774FC709774FD6F328DCE607B6530D62AD64930 79FDD5858E676690A20462C2D25B20FB1ABC44166B4C33C6051C195435CB88A0 A856906C899D3D099B0DAA9E7F8B49E661DF4626FEC3C95712E287A33208EEDC 07A64E9FA95E3541145BD5943ED36D1217A4638C684B74BE2EE5B7E1C11949AA 6810CD43303507BC69C778A8DDD19AEB8AE5C311DDA65D833A93265B1C7B8086 538E732D4615A27AD64E6167A766F575773990B5D2E5046237E86E9C0A44B3A7 FAF41A77E3F78D0AC5C805AA0B3D3EF61F720C88804A1D1B78440D1ACCBFC391 6F423AE498C24934D9AD4CB5DC16A597538E0FF64A827D015578F9FD41A1309D DDEC86857D6B7A739FF0307E654B094303728A5F1DD518DD2C540BD4563EB2B4 E37D7185406A80F0680E7821C879C0A60AF3123AB60B37553C8CA44B40F3D60F D0DEA2D45AD0D6B5 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 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 6 /Sigma put dup 8 /Phi put dup 10 /Omega put dup 11 /ff put dup 12 /fi put dup 13 /fl put dup 14 /ffi put dup 19 /acute put dup 33 /exclam put dup 34 /quotedblright put dup 35 /numbersign put dup 39 /quoteright put dup 40 /parenleft put dup 41 /parenright put dup 42 /asterisk put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 58 /colon put dup 59 /semicolon put dup 61 /equal 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 82 /R put dup 83 /S put dup 84 /T put dup 85 /U put dup 86 /V put dup 87 /W put dup 89 /Y put dup 90 /Z put dup 91 /bracketleft put dup 92 /quotedblleft put dup 93 /bracketright put dup 95 /dotaccent put dup 97 /a put dup 98 /b 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 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put dup 122 /z put dup 123 /endash put dup 125 /hungarumlaut put dup 127 /dieresis put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec 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cleartomark %%EndFont %%BeginFont: CMBX10 %!PS-AdobeFont-1.1: CMBX10 1.00B %%CreationDate: 1992 Feb 19 19:54:06 % 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 (CMBX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX10 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 46 /period put dup 48 /zero put dup 49 /one put dup 50 /two put dup 51 /three put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 56 /eight put dup 57 /nine put dup 65 /A put dup 70 /F put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 103 /g put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put dup 119 /w put readonly def /FontBBox{-301 -250 1164 946}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % 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 (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 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 45 /hyphen put dup 48 /zero put dup 51 /three put dup 56 /eight put dup 57 /nine put dup 67 /C put dup 69 /E put dup 71 /G put dup 72 /H put dup 73 /I put dup 77 /M put dup 80 /P put dup 82 /R put dup 84 /T put dup 90 /Z put dup 97 /a put dup 99 /c put dup 101 /e put dup 102 /f 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 116 /t put dup 117 /u put dup 121 /y put dup 127 /dieresis put readonly def /FontBBox{-34 -251 988 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 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cleartomark %%EndFont %%BeginFont: CMR17 %!PS-AdobeFont-1.1: CMR17 1.0 %%CreationDate: 1991 Aug 20 16:38:24 % 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 (CMR17) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR17 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 65 /A put dup 81 /Q put dup 97 /a put dup 100 /d put dup 105 /i put dup 109 /m put dup 110 /n put dup 111 /o put dup 115 /s put dup 116 /t put dup 117 /u put dup 122 /z put readonly def /FontBBox{-33 -250 945 749}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 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1080 y Fs(\006)1771 1066 y Fp(;)15 b Fl(S)1890 1080 y Fs(\006)1946 1066 y Fp(;)g Fq(G)2040 1080 y Fs(\006)2095 1066 y Fw(\))42 b(can)g(b)s(e)f(\\deformed")g(to)h(a)g(new)f(system)244 1155 y Fm(b)236 1178 y Fw(\006)e(b)m(y)g(deforming)f(its)i(kinematical) h(algebra)f Fq(A)1943 1192 y Fs(\006)2036 1178 y Fw(to)g(a)f(new)g Fr(asso)-5 b(ciative)42 b Fq(\003)p Fr(-algebr)-5 b(a)47 b Fq(A)3375 1195 y Fk(b)3369 1212 y Fs(\006)3423 1178 y Fw(,)42 b(and,)236 1291 y(corresp)s(ondingly)-8 b(,)28 b(deforming)g Fl(S)1413 1305 y Fs(\006)1495 1291 y Fw(to)h(a)f(new)f (con)m(v)m(ex)j(set)e(of)g(states)h Fl(S)2738 1308 y Fk(b)2732 1325 y Fs(\006)2787 1291 y Fw(;)f(and/or)g(b)m(y)g(deforming) 236 1404 y(the)k(symmetries)g Fq(G)928 1418 y Fs(\006)1015 1404 y Fw(to)h(a)f(new)f(set)i(of)f(symmetries)g Fq(G)2182 1421 y Fk(b)2176 1438 y Fs(\006)2231 1404 y Fw(.)45 b(In)31 b(addition,)i(a)f(class)g(of)g(structurally)236 1517 y(iden)m(tical)g(deformed)e(systems)g(ma)m(y)h(admit)g(a)g(new)f(op)s (eration)h(of)f(comp)s(osition)h Fq(_)p Fw(.)377 1630 y(F)-8 b(rom)33 b(this)e(p)s(oin)m(t)h(of)g(view,)g Fr(quantization)40 b Fw(of)32 b(a)g(classical)i(Hamiltonian)f(system)f(\006)f(consists)236 1743 y(of)38 b(deforming)g Fq(A)855 1757 y Fs(\006)947 1743 y Fw(=)f Fp(C)1127 1710 y Fn(1)1201 1743 y Fw(\(\000)1293 1757 y Fs(\006)1349 1743 y Fw(\))h(to)g(a)g(new)g(asso)s(ciativ)m(e,)k (but)37 b(usually)h(non-ab)s(elian)g Fq(\003)p Fw(-algebra)236 1856 y Fq(A)315 1873 y Fk(b)309 1889 y Fs(\006)364 1856 y Fw(,)29 b(replacing)f(the)h(P)m(oisson)f(brac)m(k)m(et)i(b)m(y)1744 1820 y Fo(i)p 1737 1835 39 4 v 1737 1887 a Fj(~)1801 1856 y Fq(\002)15 b Fw(\(comm)m(utator)32 b(of)f(elemen)m(ts)h(in)e Fq(A)3096 1873 y Fk(b)3090 1889 y Fs(\006)3144 1856 y Fw(\),)f(and,)g(corre-)236 1969 y(sp)s(ondingly)-8 b(,)36 b(passing)e(from)g Fl(S)1341 1983 y Fs(\006)1431 1969 y Fw(to)i(the)f(set)g Fl(S)1939 1986 y Fk(b)1933 2002 y Fs(\006)2023 1969 y Fw(of)g(p)s(ositiv)m(e)g(linear)g(functionals)h (on)e Fq(A)3405 1986 y Fk(b)3399 2002 y Fs(\006)3454 1969 y Fw(,)i(and)236 2082 y(replacing)j Fq(G)687 2096 y Fs(\006)780 2082 y Fw(b)m(y)f(a)h(group)f Fq(G)1324 2098 y Fk(b)1318 2115 y Fs(\006)1411 2082 y Fw(of)g Fq(\003)p Fw(-automorphisms)g(of)h Fq(A)2434 2098 y Fk(b)2428 2115 y Fs(\006)2482 2082 y Fw(.)65 b(The)37 b(parameter)i Fi(~)f Fw(\(Planc)m(k's)236 2195 y(constan)m(t\))32 b(pla)m(ys)f(the)f (role)h(of)f(the)h(\\)p Fr(deformation)k(p)-5 b(ar)g(ameter)10 b Fw(".)44 b(In)29 b(the)h(sense)h(of)f(formal)g(p)s(o)m(w)m(er)236 2308 y(series,)h(the)g(quan)m(tization)h(of)f(Hamiltonian)g(systems)g (is)f(alw)m(a)m(ys)i(p)s(ossible;)e(see)h([2,)12 b(6,)g(13].)377 2420 y(If)21 b(the)h(symmetries)g Fq(G)1131 2434 y Fs(\006)1207 2420 y Fw(of)g(a)g(ph)m(ysical)g(system)g(\006)f(are)h(describ)s(ed)e (in)h(terms)h(of)f(represen)m(tations)236 2533 y(of)j(a)h Fr(Lie)h(gr)-5 b(oup)31 b Fp(G)24 b Fw(as)h Fq(\003)p Fw(-automorphisms)e(of)i Fq(A)1881 2547 y Fs(\006)1935 2533 y Fw(,)h(the)e(symmetries)g Fq(G)2668 2550 y Fk(b)2662 2567 y Fs(\006)2741 2533 y Fw(of)g(a)h(deformation)3417 2510 y Fm(b)3409 2533 y Fw(\006)f(of)g(\006)236 2664 y(migh)m(t)k(arise)g(from)f(a)h(deformation)g(of)g(the)f(symmetry)g (group)g Fp(G)h Fw(to)g(a)g(new)f(symmetry)g(group)3583 2641 y Fm(b)3565 2664 y Fp(G)p Fw(.)236 2777 y(F)-8 b(or)32 b(example,)f(if)g Fp(G)g Fw(is)f(the)h(Galilei)i(group)d(then)1987 2754 y Fm(b)1969 2777 y Fp(G)h Fw(ma)m(y)g(b)s(e)f(the)h(P)m(oincar)m (\023)-43 b(e)33 b(group.)41 b(In)30 b(this)g(w)m(ell)236 2890 y(kno)m(wn)k(example,)j(the)d(deformation)h(parameter)g(is)g Fp(c)2161 2857 y Fn(\000)p Fs(1)2290 2890 y Fw(\(the)g(in)m(v)m(erse)g (of)g(the)f(sp)s(eed)g(of)h(ligh)m(t\).)236 3003 y(Another)c(example)h (is)f(encoun)m(tered)g(if)g(one)g(replaces)h(the)f(symmetry)g(group)f (of)h(translations)h(of)236 3115 y(a)c(c)m(harged)h(particle)g (con\014ned)d(to)j(a)f(plane)g Fi(R)1812 3082 y Fs(2)1878 3115 y Fw(b)m(y)g(the)g(non-comm)m(utativ)m(e)i(Heisen)m(b)s(erg)e (group)f(of)236 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Fs(\006)1589 4039 y Fv(1)1623 4030 y Fn(_)1676 4013 y Fk(b)1670 4030 y Fs(\006)1721 4039 y Fv(1)1810 3993 y Fw(:)1835 3996 y(=)51 b Fq(A)2036 4013 y Fk(b)2030 4030 y Fs(\006)2081 4039 y Fv(1)2139 3996 y Fq(\012)20 b(A)2309 4013 y Fk(b)2303 4030 y Fs(\006)2354 4039 y Fv(2)2408 3996 y Fp(:)1112 b Fw(\(5\))236 4199 y(If)30 b(\006)393 4213 y Fs(1)432 4199 y Fp(;)15 b(:)g(:)g(:)i(;)e Fw(\006)700 4213 y Fo(n)777 4199 y Fw(are)31 b Fr(identic)-5 b(al)41 b Fw(systems,)30 b(\006)1729 4213 y Fo(j)1791 4199 y Fq(')25 b Fw(\006)30 b(for)g Fp(j)h Fw(=)25 b(1)p Fp(;)15 b(:)g(:)g(:)i(;)e(n)p Fw(,)30 b(then)1271 4403 y Fq(A)1350 4419 y Fk(b)1344 4436 y Fs(\006)1395 4445 y Fv(1)1429 4436 y Fn(_\001\001\001)o(_)1588 4419 y Fk(b)1582 4436 y Fs(\006)1633 4444 y Fh(n)1730 4403 y Fw(=)51 b Fq(A)1931 4419 y Fk(b)1925 4436 y Fs(\006)1976 4445 y Fv(1)2034 4403 y Fq(\012)2105 4417 y Fo(s)2162 4403 y Fq(\001)15 b(\001)g(\001)21 b(\012)2359 4417 y Fo(s)2416 4403 y Fq(A)2495 4419 y Fk(b)2489 4436 y Fs(\006)2540 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Fr(statistics)7 b Fw(")42 b(of)1307 5148 y Fm(b)1299 5171 y Fw(\006)e(\(Bose-,)45 b(F)-8 b(ermi-,)44 b(or)c(fractional)i(statistics\).)73 b(See)40 b([3,)19 b(7])41 b(for)f(a)236 5283 y(general)32 b(analysis.)377 5396 y(A)41 b(quan)m(tum)f(system)1200 5373 y Fm(b)1192 5396 y Fw(\006)h(with)f(fractional)i(statistics,)k(i.e.,)f(whose)40 b(quan)m(tum)h(statistics)h(is)236 5509 y(describ)s(ed)25 b(b)m(y)h(represen)m(tations)h(of)f(the)g(braid)f(groups,)h(ma)m(y)h (ha)m(v)m(e)g(symmetries)f Fq(G)3113 5526 y Fk(b)3107 5543 y Fs(\006)3188 5509 y Fw(describ)s(ed)f(in)236 5622 y(terms)g(of)g(represen)m(tations)g(of)g(some)g(\\quan)m(tum)g(group".) 38 b(Man)m(y)26 b(examples)f(of)g(quan)m(tum)f(groups)p Black 1926 5871 a(4)p Black eop end %%Page: 5 5 TeXDict begin 5 4 bop Black Black 236 162 a Fw(arise)37 b(as)g(asso)s(ciativ)m(e)i(deformations)e(of)g(the)f(univ)m(ersal)h(en) m(v)m(eloping)h(algebra)g(of)e(a)h(Lie)g(algebra)236 275 y(with)30 b(the)h(structure)f(of)g(a)h(quasi-triangular)g(Hopf)f 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b(c-)236 1291 y(ond\))36 b(quantizations")f(of)g(c)-5 b(ontinuum)34 b(the)-5 b(ories)36 b(of)f(matter)p Fw(,)f(the)e(deformation)g(theory)h(in)m(v)m(olv)m(ed) 236 1404 y(b)s(eing)24 b(the)g(one)g(of)g(asso)s(ciativ)m(e)i Fq(\003)p Fw(-algebras.)41 b(Although)24 b(this)f(p)s(oin)m(t)h(of)g (view)g(has)g(b)s(een)f(around,)i(at)236 1517 y(least)k(implicitly)-8 b(,)29 b(for)f(a)f(long)h(time,)h(it)f(has)f(rarely)g(b)s(een)g (emphasized)g(explicitly)-8 b(.)42 b(As)27 b(men)m(tioned)236 1630 y(ab)s(o)m(v)m(e,)g(it)e(underlies)f(Einstein's)g(theory)g(of)h (photons.)38 b(More)25 b(generally)-8 b(,)28 b(an)m(y)c(quan)m(tum)g (\014eld)g(the-)236 1743 y(ory)j(that)g(is)f(the)h(quan)m(tization)i (of)d(a)h(classical)i(Hamiltonian)f(\014eld)e(theory)h(pro)m(vides)f (an)h(example)236 1856 y(of)j(this)g(p)s(oin)m(t)h(of)f(view.)41 b(In)29 b(this)h(note,)h(w)m(e)g(illustrate)g(it)g(in)e(terms)h(of)h (the)f(theory)g(of)g(in)m(teracting)236 1969 y(\(classical)35 b(and)c(quan)m(tum\))h(gases.)46 b(W)-8 b(e)33 b(fo)s(cus)e(on)h(the)g (discussion)f(of)i(quan)m(tum)e(gases.)46 b(A)32 b(more)236 2082 y(complete)g(discussion)e(that)h(also)g(includes)f(classical)j (gases)e(and)f(\015uids)f(will)h(app)s(ear)g(elsewhere.)377 2195 y(A)44 b(glimpse)f(of)g(the)h(idea)f(that)h(Quan)m(tum)f(Theory)f (and)h(A)m(tomism)h(ma)m(y)g(b)s(e)e(inseparable)236 2308 y(companions)33 b(ma)m(y)h(b)s(e)f(gained)g(b)m(y)g(studying)g (the)g(classical)i(statistical)h(mec)m(hanics)e(of)g(iden)m(tical)236 2420 y(particles:)41 b(The)27 b(Liouville)i(measure)f(on)g(the)g(phase) f(space)i(of)f(suc)m(h)f(systems)h(has)g(the)g(dimension)236 2533 y(\(action)r(\))549 2500 y Fo(f)595 2533 y Fw(,)f(where)f Fp(f)36 b Fw(is)27 b(the)g(n)m(um)m(b)s(er)e(of)i(degrees)g(of)f (freedom.)40 b(In)26 b(order)g(to)h(de\014ne)f(the)h(partition)236 2646 y(functions)39 b(of)h(suc)m(h)f(systems)h(as)f(dimensionless)h (quan)m(tities,)j(one)d(m)m(ust)f(divide)h(the)f(Liouville)236 2759 y(measure)26 b(b)m(y)h(the)f Fp(f)916 2726 y Fs(th)1013 2759 y Fw(p)s(o)m(w)m(er)g(of)g(a)h(constan)m(t)h(\()p Fp(h)p Fw(\))f(with)f(the)h(dimension)f(of)g(an)g(action.)41 b(Moreo)m(v)m(er,)236 2872 y(in)f(order)f(for)h(the)h(basic)f(thermo)s (dynamic)f(p)s(oten)m(tials)j(to)f(b)s(e)e(extensiv)m(e,)44 b(one)d(m)m(ust)e(consider)236 2985 y(iden)m(tical)44 b(particles)g(to)f(b)s(e)f Fr(indistinguishable)50 b Fw(and)42 b(divide)h(the)f(partition)i(functions)e(b)m(y)g Fp(N)10 b Fw(!,)236 3098 y(where)30 b Fp(N)40 b Fw(is)31 b(the)f(n)m(um)m(b)s(er)f(of)i(particles)g({)g(as)g(\014rst)e (recognized)j(b)m(y)e(Gibbs.)377 3211 y(F)-8 b(or)32 b(the)g(purp)s(oses)d(of)j(this)f(note,)i(a)e Fr(classic)-5 b(al)35 b(gas)40 b Fw(is)31 b(describ)s(ed)f(as)i(a)g Fr(c)-5 b(ontinuous)34 b(me)-5 b(dium)p Fw(,)236 3324 y(whose)30 b(states)i(are)e(giv)m(en)i(b)m(y)e(sp)s(ecifying)g(a)h Fr(mass)i(density)p Fw(,)f Fp(d\026)p Fw(\()p Fp(x;)15 b(p)p Fw(\))26 b(=)f Fp(M)10 b(f)g Fw(\()p Fp(x;)15 b(p)p Fw(\))g Fp(dx)g(dp)p Fw(,)31 b(on)f(the)236 3437 y(Cartesian)39 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y Fw([)p Fp(f)10 b Fw(]\()p Fp(x)p Fw(\))1385 5048 y(:)1411 5051 y(=)50 b Fp(V)20 b Fw(\()p Fp(x)p Fw(\))h(+)1839 4927 y Fm(Z)1945 5051 y Fp(dy)d(\036)p Fw(\()p Fp(x)j Fq(\000)f Fp(y)s Fw(\))2406 4927 y Fm(Z)2512 5051 y Fp(dp)15 b(f)10 b Fw(\()p Fp(y)s(;)15 b(p)p Fw(\))g Fp(:)626 b Fw(\(9\))236 5283 y(Here)29 b Fp(V)48 b Fw(is)28 b(the)g(p)s(oten)m(tial)h(of)f(external)h(forces)f (acting)h(on)f(the)g(gas)g(and)g Fp(\036)g Fw(a)g(t)m(w)m(o-b)s(o)s(dy) g(p)s(oten)m(tial)236 5396 y(describing)i(self-in)m(teractions)j(of)e (the)f(gas.)377 5509 y(The)25 b(Vlaso)m(v)h(equation)g(arises)f(as)g (the)g(mean-\014eld)g(limit)h(of)f(a)g(classical)i(Hamiltonian)f (system)236 5622 y(of)40 b Fp(n)h Fw(=)f Fp(\027)6 b(N)50 b Fw(p)s(oin)m(t)40 b(particles)h(of)f(mass)f Fp(m)i Fw(=)g Fp(M)5 b(=)-5 b(N)10 b Fw(,)43 b(with)c(tra)5 b(jectories)42 b(\()p Fp(x)3004 5636 y Fo(j)3041 5622 y Fw(\()p Fp(t)p Fw(\)\))3179 5589 y Fo(n)3179 5648 y(j)t Fs(=1)3306 5622 y Fw(,)h(mo)m(ving)p Black 1926 5871 a(5)p Black 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b(N)47 b Fw(is)36 b(a)h(dimensionless)236 3240 y(coupling)21 b(constan)m(t.)39 b(The)21 b(dynamics)f(of)i(the)f (system)g(is)g(describ)s(ed)f(b)m(y)h(the)g(Sc)m(hr\177)-45 b(odinger)21 b(equation)1190 3455 y Fp(i@)1269 3469 y Fo(t)1299 3455 y Fp(')1358 3407 y Fs(\()p Fo(n)p Fs(\))1358 3479 y Fo(t)1511 3455 y Fw(=)50 b Fp(H)1715 3407 y Fs(\()p Fo(n)p Fs(\))1708 3484 y Fo(N)1817 3455 y Fp(')1876 3407 y Fs(\()p Fo(n)p Fs(\))1876 3479 y Fo(t)1993 3455 y Fp(;)198 b(')2275 3407 y Fs(\()p Fo(n)p Fs(\))2275 3479 y Fo(t)2402 3455 y Fq(2)25 b(H)2566 3418 y Fs(\()p Fo(n)p Fs(\))2683 3455 y Fp(:)792 b Fw(\(24\))377 3659 y(The)30 b(mean-\014eld)f(limit)i (is)f(the)f(limit)i(where)e Fp(n;)15 b(N)35 b Fq(!)26 b(1)j Fw(in)h(suc)m(h)f(a)h(w)m(a)m(y)h(that)f Fp(n=)-5 b(N)35 b Fw(=)25 b Fp(O)s Fw(\(1\).)236 3772 y(The)i(ph)m(ysical)h (meaning)g(of)g(this)f(limit)i(is)e(most)h(transparen)m(t)g(if)f(the)h (system)g(is)f(describ)s(ed)g(in)g(the)236 3885 y(formalism)k(of)f (second)h(quan)m(tization.)42 b(F)-8 b(o)s(c)m(k)32 b(space)f(is)g(the) f(Hilb)s(ert)g(space)h(giv)m(en)h(b)m(y)1627 4154 y Fq(F)1752 4151 y Fw(:)1777 4154 y(=)1932 4040 y Fn(1)1898 4067 y Fm(M)1900 4262 y Fo(n)p Fs(=0)2051 4154 y Fq(H)2129 4116 y Fs(\()p Fo(n)p Fs(\))2245 4154 y Fp(:)1230 b Fw(\(25\))236 4450 y(Subspaces)30 b Fq(F)741 4417 y Fn(\024)p Fo(k)869 4450 y Fw(of)g(\014nite)h(particle)g(n)m(um)m(b)s(er)e(are)i(de\014ned) e(b)m(y)1578 4736 y Fq(F)1652 4698 y Fn(\024)p Fo(k)1801 4733 y Fw(:)1826 4736 y(=)1996 4622 y Fo(k)1947 4649 y Fm(M)1949 4844 y Fo(n)p Fs(=0)2100 4736 y Fq(H)2178 4698 y Fs(\()p Fo(n)p Fs(\))2294 4736 y Fp(:)1181 b Fw(\(26\))236 5021 y(F)-8 b(o)s(c)m(k)32 b(space)e Fq(F)40 b Fw(carries)30 b(a)h(represen)m(tation)g(of)f(the)h(canonical)g(comm)m(utation)h (relations)f(\(CCR\):)1149 5225 y([)1190 5201 y Fm(b)1174 5225 y Fp( )1233 5239 y Fo(N)1301 5225 y Fw(\()p Fp(x)p Fw(\))p Fp(;)1480 5201 y Fm(b)1463 5225 y Fp( )1522 5239 y Fo(N)1590 5225 y Fw(\()p Fp(y)s Fw(\)])52 b(=)e([)1947 5201 y Fm(b)1931 5225 y Fp( )1993 5187 y Fn(\003)1990 5247 y Fo(N)2058 5225 y Fw(\()p Fp(x)p Fw(\))p Fp(;)2237 5201 y Fm(b)2220 5225 y Fp( )2282 5187 y Fn(\003)2279 5247 y Fo(N)2347 5225 y Fw(\()p Fp(y)s Fw(\)])h(=)g(0)15 b Fp(;)706 b Fw(\(27a\))1149 5412 y([)1190 5388 y Fm(b)1174 5412 y Fp( )1233 5426 y Fo(N)1301 5412 y Fw(\()p Fp(x)p Fw(\))p Fp(;)1480 5388 y Fm(b)1463 5412 y Fp( )1525 5374 y Fn(\003)1522 5434 y Fo(N)1590 5412 y Fw(\()p Fp(y)s Fw(\)])52 b(=)1935 5351 y(1)p 1916 5391 V 1916 5474 a Fp(N)2024 5412 y(\016)s Fw(\()p Fp(x)21 b Fq(\000)f Fp(y)s Fw(\))15 b Fp(;)1060 b Fw(\(27b\))p Black 236 5536 1371 4 v 340 5590 a Fv(2)374 5621 y Fu(Here,)26 b(and)g(in)f(the)h(follo)n (wing,)i(w)n(e)e(w)n(ork)g(in)g(units)f(suc)n(h)g(that)h Fg(~)21 b Fu(=)g(1.)p Black Black 1926 5871 a Fw(8)p Black eop end %%Page: 9 9 TeXDict begin 9 8 bop Black Black 236 162 a Fw(with)462 138 y Fm(b)446 162 y Fp( )505 176 y Fo(N)573 162 y Fw(\()p Fp(x)p Fw(\)\012)31 b(=)f(0,)35 b(for)e(all)h Fp(x;)15 b(y)34 b Fq(2)c Fi(R)1597 129 y Fs(3)1636 162 y Fw(,)k(where)f(\012)d (=)h(\(1)p Fp(;)15 b Fw(0)p Fp(;)g Fw(0)p Fp(;)g(:)g(:)g(:)k Fw(\))31 b Fq(2)f(F)42 b Fw(is)34 b(the)g(v)-5 b(acuum.)49 b(Note)236 275 y(that)29 b(the)f(creation)i(and)d(annihilation)i(op)s (erators,)2051 251 y Fm(b)2035 275 y Fp( )2097 242 y Fn(\003)2094 302 y Fo(N)2162 275 y Fw(\()p Fp(x)p Fw(\),)2354 251 y Fm(b)2338 275 y Fp( )2397 289 y Fo(N)2465 275 y Fw(\()p Fp(x)p Fw(\),)g(are)g(rescaled)f(b)m(y)h(a)f(factor)h(of)236 388 y Fp(N)319 355 y Fn(\000)p Fs(1)p Fo(=)p Fs(2)518 388 y Fw(as)34 b(compared)f(to)i(the)f(usual)f(ones.)51 b(This)33 b(accoun)m(ts)i(for)e(the)h(factor)h(1)p Fp(=)-5 b(N)45 b Fw(in)33 b(the)h(CCR,)236 501 y(in)27 b(analogy)i(to)g(the)e (usual)g Fi(~)p Fw(.)40 b(Th)m(us)26 b(1)p Fp(=)-5 b(N)39 b Fw(is)27 b(giv)m(en)h(the)g(role)g(of)g(a)g(deformation)g(parameter.) 40 b(The)236 614 y(direct)c(sum)f(of)g(the)h(Hamiltonians)g(\(22\))r(,) h(acting)g(on)e(F)-8 b(o)s(c)m(k)37 b(space)f(and)f(rescaled)h(b)m(y)f 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Fo(N)2368 1426 y Fw(\()p Fp(x)p Fw(\))15 b Fp(dx)g(;)856 b Fw(\(29\))906 1645 y Fm(b)871 1670 y Fl(V)928 1684 y Fo(N)1045 1667 y Fw(:)1070 1670 y(=)1201 1608 y(1)p 1201 1649 46 4 v 1201 1732 a(2)1272 1546 y Fm(Z)1378 1670 y Fp(dx)1492 1546 y Fm(Z)1598 1670 y Fp(dy)1735 1646 y Fm(b)1719 1670 y Fp( )1781 1632 y Fn(\003)1778 1692 y Fo(N)1845 1670 y Fw(\()p Fp(x)p Fw(\))1984 1646 y Fm(b)1967 1670 y Fp( )2029 1632 y Fn(\003)2026 1692 y Fo(N)2094 1670 y Fw(\()p Fp(y)s Fw(\))15 b Fp(\036)p Fw(\()p Fp(x)22 b Fq(\000)e Fp(y)s Fw(\))2595 1646 y Fm(b)2579 1670 y Fp( )2638 1684 y Fo(N)2705 1670 y Fw(\()p Fp(y)s Fw(\))2840 1646 y Fm(b)2823 1670 y Fp( )2882 1684 y Fo(N)2950 1670 y Fw(\()p Fp(x)p Fw(\))15 b Fp(:)388 b Fw(\(30\))236 1889 y(Th)m(us)30 b(the)g(Sc)m(hr\177)-45 b(odinger)30 b(equations)h(\(24\))r(,)f(with)g Fp(n)25 b Fw(=)g(0)p Fp(;)15 b Fw(1)p Fp(;)g Fw(2)p Fp(;)g(:)g(:)g(:)k Fw(,)31 b(imply)f(the)g(equation)1349 2044 y Fp(i)p 1323 2085 83 4 v 1323 2168 a(N)1431 2106 y(@)1479 2120 y 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Fs(\))1229 4622 y Fw(:)1255 4625 y(=)g Fp(P)1422 4639 y Fs(s)1469 4625 y Fw(\()p Fp(a)1552 4592 y Fs(\()p Fo(p)p Fs(\))1672 4625 y Fq(\012)26 b Ff(1)1823 4592 y Fs(\()p Fo(q)r Fn(\000)p Fo(l)q Fs(\))1992 4625 y Fw(\))15 b(\()p Ff(1)2131 4592 y Fs(\()p Fo(p)p Fn(\000)p Fo(l)q Fs(\))2328 4625 y Fq(\012)25 b Fp(b)2463 4592 y Fs(\()p Fo(q)r Fs(\))2556 4625 y Fw(\))38 b(is)g(a)h(b)s(ounded) d(op)s(erator)i(on)463 4787 y Fq(H)541 4754 y Fs(\()p Fo(p)p Fs(+)p Fo(q)r Fn(\000)p Fo(l)q Fs(\))801 4787 y Fw(.)i(Here)30 b Fp(P)1138 4801 y Fs(s)1199 4787 y Fw(is)e(the)h(orthogonal)h(pro)5 b(jection)30 b(on)m(to)g(the)e (subspace)h(of)f(v)m(ectors)j(sym-)463 4900 y(metric)h(under)c(the)j (exc)m(hange)h(of)e(particles.)42 b(In)30 b(terms)g(of)h(op)s(erator)f (k)m(ernels)h(this)f(reads)769 5077 y(\()p Fp(a)852 5040 y Fs(\()p Fo(p)p Fs(\))972 5077 y Fp(*)1006 5138 y Fo(l)1103 5077 y Fp(b)1142 5040 y Fs(\()p Fo(q)r Fs(\))1235 5077 y Fw(\)\()p Fp(x)1357 5091 y Fs(1)1397 5077 y Fp(;)15 b(:)g(:)g(:)i(x)1611 5092 y Fo(p)p Fs(+)p Fo(q)r Fn(\000)p Fo(l)1816 5077 y Fw(;)e Fp(y)1901 5091 y Fs(1)1940 5077 y Fp(;)g(:)g(:)g(:)i(;)e(y)2187 5092 y Fo(p)p Fs(+)p Fo(q)r Fn(\000)p Fo(l)2392 5077 y Fw(\))654 5350 y(=)50 b Fp(P)833 5364 y Fs(s)880 5226 y Fm(Z)1033 5236 y Fo(l)986 5263 y Fm(Y)987 5459 y Fo(i)p Fs(=1)1118 5350 y Fp(du)1217 5364 y Fo(i)1270 5350 y Fp(a)1318 5312 y Fs(\()p Fo(p)p Fs(\))1413 5350 y Fw(\()p Fp(x)1500 5364 y Fs(1)1540 5350 y Fp(;)15 b(:)g(:)g(:)h(;)f(x)1793 5364 y Fo(p)1833 5350 y Fw(;)g Fp(y)1918 5364 y Fs(1)1958 5350 y Fp(;)g(:)g(:)g(:)h(;)f (y)2204 5365 y Fo(p)p Fn(\000)p Fo(l)2321 5350 y Fp(;)g(u)2413 5364 y Fs(1)2453 5350 y Fp(;)g(:)g(:)g(:)h(;)f(u)2706 5365 y Fo(l)2733 5350 y Fw(\))1225 5588 y Fq(\001)20 b Fp(b)1309 5551 y Fs(\()p Fo(q)r Fs(\))1402 5588 y Fw(\()p Fp(u)1489 5602 y Fs(1)1529 5588 y Fp(;)15 b(:)g(:)g(:)i(;)e(u)1783 5603 y Fo(l)1809 5588 y Fp(;)g(x)1901 5602 y Fo(p)p Fs(+1)2031 5588 y Fp(;)g(:)g(:)g(:)i(;)e(x)2285 5603 y Fo(p)p Fs(+)p Fo(q)r Fn(\000)p Fo(l)2491 5588 y Fw(;)g Fp(y)2576 5603 y Fo(p)p Fn(\000)p Fo(l)q Fs(+1)2782 5588 y Fp(;)g(:)g(:)g(:)i(;)e(y) 3029 5603 y Fo(p)p Fs(+)p Fo(q)r Fn(\000)p Fo(l)3234 5588 y Fw(\))g Fp(:)191 b Fw(\(35\))p Black 1926 5871 a(9)p Black eop end %%Page: 10 10 TeXDict begin 10 9 bop Black Black Black 297 162 a Fw(\(ii\))p Black 46 w(An)30 b(immediate)i(consequence)f(of)g(\(i\))g(is)796 388 y Fm(\002)855 439 y(b)833 462 y Fp(A)901 476 y Fo(N)969 462 y Fw(\()p Fp(a)1052 424 y Fs(\()p Fo(p)p Fs(\))1147 462 y Fw(\))p Fp(;)1259 439 y Fm(b)1238 462 y Fp(A)1306 476 y Fo(N)1373 462 y Fw(\()p Fp(b)1447 424 y Fs(\()p Fo(q)r Fs(\))1540 462 y Fw(\))1576 388 y Fm(\003)1664 462 y Fw(=)1785 340 y Fs(min\()p Fo(p;q)r Fs(\))1850 376 y Fm(X)1860 573 y Fo(l)q Fs(=1)2062 334 y Fm(\022)2129 400 y Fp(p)2137 524 y(l)2175 334 y Fm(\023\022)2309 400 y Fp(q)2316 524 y(l)2352 334 y Fm(\023)2457 400 y Fp(l)r Fw(!)p 2429 441 109 4 v 2429 524 a Fp(N)2512 498 y Fo(l)2585 439 y Fm(b)2563 462 y Fp(A)2631 476 y Fo(N)2699 388 y Fm(\000)o(\002)2778 462 y Fp(a)2826 424 y Fs(\()p Fo(p)p Fs(\))2946 462 y Fp(*)2981 523 y Fo(l)3077 462 y Fp(b)3116 424 y Fs(\()p Fo(q)r Fs(\))3209 388 y Fm(\003\001)3304 462 y Fp(;)171 b Fw(\(36\))463 761 y(where)726 687 y Fm(\002)764 761 y Fp(a)812 728 y Fs(\()p Fo(p)p Fs(\))932 761 y Fp(*)967 822 y Fo(l)1063 761 y Fp(b)1102 728 y Fs(\()p Fo(q)r Fs(\))1195 687 y Fm(\003)1259 758 y Fw(:)1284 761 y(=)25 b Fp(a)1428 728 y Fs(\()p Fo(p)p Fs(\))1548 761 y Fp(*)1582 822 y Fo(l)1679 761 y Fp(b)1718 728 y Fs(\()p Fo(q)r Fs(\))1831 761 y Fq(\000)20 b Fp(b)1961 728 y Fs(\()p Fo(q)r Fs(\))2079 761 y Fp(*)2114 822 y Fo(l)2210 761 y Fp(a)2258 728 y Fs(\()p Fo(p)p Fs(\))2353 761 y Fw(.)p Black 272 1002 a(\(iii\))p Black 485 979 a Fm(b)463 1002 y Fp(A)531 1016 y Fo(N)599 1002 y Fw(\()p Fp(a)682 969 y Fs(\()p Fo(p)p Fs(\))777 1002 y Fw(\))812 969 y Fn(\003)877 1002 y Fw(=)994 979 y Fm(b)973 1002 y Fp(A)1041 1016 y Fo(N)1108 1002 y Fw(\()p Fp(a)1191 969 y Fs(\()p Fo(p)p Fs(\))p Fn(\003)1322 1002 y Fw(\),)30 b(where)970 1215 y Fp(a)1018 1177 y Fs(\()p Fo(p)p Fs(\))p Fn(\003)1148 1215 y Fw(\()p Fp(x)1235 1229 y Fs(1)1275 1215 y Fp(;)15 b(:)g(:)g(:)h(;)f(x)1528 1229 y Fo(p)1568 1215 y Fw(;)g Fp(y)1653 1229 y Fs(1)1693 1215 y Fp(;)g(:)g(:)g(:)h(y) 1899 1229 y Fo(p)1939 1215 y Fw(\))51 b(=)p 2146 1128 969 4 v 50 w Fp(a)2194 1188 y Fs(\()p Fo(p)p Fs(\))2288 1215 y Fw(\()p Fp(y)2368 1229 y Fs(1)2408 1215 y Fp(;)15 b(:)g(:)g(:)h(;)f(y)2654 1229 y Fo(p)2694 1215 y Fw(;)g Fp(x)2786 1229 y Fs(1)2826 1215 y Fp(;)g(:)g(:)g(:)h(x)3039 1229 y Fo(p)3079 1215 y Fw(\))g Fp(:)345 b Fw(\(37\))p Black 274 1463 a(\(iv\))p Black 46 w(On)30 b(the)h(subspaces)e Fq(F)1261 1430 y Fn(\024)p Fo(k)1389 1463 y Fw(of)i(b)s(ounded)d (particle)k(n)m(um)m(b)s(er,)2571 1440 y Fm(b)2549 1463 y Fp(A)2617 1477 y Fo(N)2684 1463 y Fw(\()p Fp(a)2767 1430 y Fs(\()p Fo(p)p Fs(\))2862 1463 y Fw(\))f(is)g(b)s(ounded)d(and) 1446 1581 y Fm(\015)1446 1636 y(\015)1446 1690 y(\015)1518 1663 y(b)1497 1686 y Fp(A)1565 1700 y Fo(N)1632 1686 y Fw(\()p Fp(a)1715 1648 y Fs(\()p Fo(p)p Fs(\))1810 1686 y Fw(\))1845 1581 y Fm(\014)1845 1636 y(\014)1845 1690 y(\014)1876 1749 y Fn(F)1933 1730 y Fe(\024)p Fh(\027)s(N)2077 1581 y Fm(\015)2077 1636 y(\015)2077 1690 y(\015)2178 1686 y Fq(\024)50 b Fp(\027)2350 1648 y Fo(p)2405 1686 y Fq(k)p Fp(a)2498 1648 y Fs(\()p Fo(p)p Fs(\))2593 1686 y Fq(k)15 b Fp(:)822 b Fw(\(38\))236 1970 y(F)-8 b(urthermore,)38 b(the)e(op)s(erators)h(in)1507 1947 y Fm(b)1478 1970 y Fq(A)f Fw(are)h(gauge-in)m(v)-5 b(arian)m(t:)55 b(Under)35 b(the)h Fq(\003)p Fw(-automorphism)g Fp(\034)3597 1985 y Fo(\022)3636 1970 y Fw(,)236 2083 y(giv)m(en)c(b)m(y)865 2196 y Fp(\034)905 2211 y Fo(\022)944 2196 y Fw(\()995 2172 y Fm(b)979 2196 y Fp( )1038 2210 y Fo(N)1106 2196 y Fw(\()p Fp(x)p Fw(\)\))1314 2193 y(:)1340 2196 y(=)50 b Fp(e)1503 2159 y Fn(\000)p Fo(i\022)1637 2172 y Fm(b)1621 2196 y Fp( )1680 2210 y Fo(N)1748 2196 y Fw(\()p Fp(x)p Fw(\))197 b Fp(\034)2107 2211 y Fo(\022)2146 2196 y Fw(\()2197 2172 y Fm(b)2181 2196 y Fp( )2243 2159 y Fn(\003)2240 2219 y Fo(N)2308 2196 y Fw(\()p Fp(x)p Fw(\)\))51 b(=)f Fp(e)2679 2159 y Fo(i\022)2759 2172 y Fm(b)2743 2196 y Fp( )2805 2159 y Fn(\003)2802 2219 y Fo(N)2869 2196 y Fw(\()p Fp(x)p Fw(\))15 b Fp(;)469 b Fw(\(39\))236 2361 y(w)m(e)41 b(ha)m(v)m(e)h Fp(\034)640 2376 y Fo(\022)679 2361 y Fw(\()736 2338 y Fm(b)714 2361 y Fp(A)p Fw(\))h(=)995 2338 y Fm(b)973 2361 y Fp(A)p Fw(,)h(for)c(all)1417 2338 y Fm(b)1396 2361 y Fp(A)i Fq(2)1638 2338 y Fm(b)1609 2361 y Fq(A)p Fw(.)71 b(Note)42 b(that)f(\()p Fp(\034)2290 2376 y Fo(\022)2330 2361 y Fw(\))2365 2376 y Fo(\022)r Fn(2)p Fj(R)2540 2361 y Fw(can)f(b)s(e)g(implemen)m(ted)i(b)m(y)e(the) 236 2474 y(one-parameter)32 b(unitary)e(group)g(\()p Fp(U)10 b Fw(\()p Fp(\022)s Fw(\)\))1675 2489 y Fo(\022)r Fn(2)p Fj(R)1839 2474 y Fw(on)31 b Fq(F)39 b Fw(generated)32 b(b)m(y)e(the)h(n)m(um)m(b)s(er)e(op)s(erator)1432 2692 y Fm(c)1385 2716 y Fl(N)1524 2713 y Fw(:)1549 2716 y(=)c Fp(N)1743 2593 y Fm(Z)1850 2716 y Fp(dx)1990 2692 y Fm(b)1974 2716 y Fp( )2036 2679 y Fn(\003)2033 2739 y Fo(N)2101 2716 y Fw(\()p Fp(x)p Fw(\))2239 2692 y Fm(b)2223 2716 y Fp( )2282 2730 y Fo(N)2350 2716 y Fw(\()p Fp(x)p Fw(\))15 b Fp(:)988 b Fw(\(40\))236 3022 y Ft(3)135 b(A)44 b(Hamiltonian)j(Con)l (tin)l(uum)f(Theory)e(of)h(Gases)236 3225 y Fw(In)39 b(this)g(section,)j(w)m(e)e(consider)f(a)g(\\classical")j(Hamiltonian)f (system)e(with)g(phase)f(space)i(\000)g(=)236 3338 y Fp(H)319 3305 y Fs(1)312 3365 y(W)388 3338 y Fw(\()p Fi(R)489 3305 y Fs(3)529 3338 y Fw(\),)33 b(a)g(w)m(eigh)m(ted)h (complex)f(Sob)s(olev)f(space)h(of)g(index)f(1,)i(de\014ned)d(as)h(the) h(quadratic)g(form)236 3451 y(domain)j(of)g(the)f(op)s(erator)h Fq(\000)1307 3415 y Fs(\001)p 1288 3430 98 4 v 1288 3482 a(2)p Fo(m)1419 3451 y Fw(+)24 b Fp(V)c Fw(.)56 b(On)35 b(\000)h(w)m(e)g(use)f(complex)h(co)s(ordinates)h Fp( )s Fw(\()p Fp(x)p Fw(\))p Fp(;)p 3293 3377 63 4 v 15 w( )5 b Fw(\()p Fp(x)p Fw(\))36 b(and)236 3564 y(de\014ne)30 b(a)h(P)m(oisson)g(brac)m(k)m(et)h Fq(f)15 b(\001)g Fp(;)31 b Fq(\001)16 b(g)30 b Fw(through)1237 3764 y Fq(f)p Fp( )s Fw(\()p Fp(x)p Fw(\))p Fp(;)15 b( )s Fw(\()p Fp(y)s Fw(\))s Fq(g)51 b Fw(=)f Fq(f)p 1951 3690 V Fp( )t Fw(\()p Fp(x)p Fw(\))p Fp(;)p 2176 3690 V 15 w( )t Fw(\()p Fp(y)s Fw(\))q Fq(g)h Fw(=)f(0)15 b Fp(;)794 b Fw(\(41a\))1237 3913 y Fq(f)p Fp( )s Fw(\()p Fp(x)p Fw(\))p Fp(;)p 1506 3839 V 15 w( )5 b Fw(\()p Fp(y)s Fw(\))q Fq(g)51 b Fw(=)f Fp(i)15 b(\016)s Fw(\()p Fp(x)22 b Fq(\000)e Fp(y)s Fw(\))15 b Fp(:)1131 b Fw(\(41b\))236 4113 y(A)31 b(Hamilton)g(functional)g(is)f (de\014ned)g(b)m(y)1271 4314 y Fl(H)d Fw(\()p 1421 4240 V Fp( )t(;)15 b( )s Fw(\))52 b(=)e Fl(H)1882 4328 y Fs(0)1921 4314 y Fw(\()p 1956 4240 V Fp( )t(;)15 b( )s Fw(\))22 b(+)e Fl(V)k Fw(\()p 2385 4240 V Fp( )t(;)15 b( )s Fw(\))g Fp(;)875 b Fw(\(42\))236 4514 y(where)929 4742 y Fl(H)1017 4756 y Fs(0)1056 4742 y Fw(\()p 1091 4668 V Fp( )t(;)15 b( )s Fw(\))1343 4739 y(:)1368 4742 y(=)1489 4618 y Fm(Z)1595 4742 y Fp(dx)p 1720 4668 V 26 w( )s Fw(\()p Fp(x)p Fw(\))1904 4614 y Fm(\024)1953 4742 y Fq(\000)2073 4681 y Fw(1)p 2034 4721 126 4 v 2034 4804 a(2)p Fp(m)2169 4742 y Fw(\001)20 b(+)g Fp(V)g Fw(\()p Fp(x)p Fw(\))2551 4614 y Fm(\025)2599 4742 y Fp( )s Fw(\()p Fp(x)p Fw(\))717 b(\(43\))975 4985 y Fl(V)24 b Fw(\()p 1091 4911 63 4 v Fp( )t(;)15 b( )s Fw(\))1343 4982 y(:)1368 4985 y(=)1499 4924 y(1)p 1499 4964 46 4 v 1499 5048 a(2)1570 4862 y Fm(Z)1676 4985 y Fp(dx)1790 4862 y Fm(Z)1896 4985 y Fp(dy)29 b Fq(j)p Fp( )s Fw(\()p Fp(x)p Fw(\))p Fq(j)2251 4948 y Fs(2)2307 4985 y Fp(\036)p Fw(\()p Fp(x)21 b Fq(\000)e Fp(y)s Fw(\))c Fq(j)p Fp( )s Fw(\()p Fp(y)s Fw(\))p Fq(j)2887 4948 y Fs(2)2944 4985 y Fp(:)531 b Fw(\(44\))236 5223 y(The)37 b(Hamiltonian)j(equations)e(of)g(motion)h(corresp)s(onding)d(to)j Fl(H)65 b Fw(are)38 b(giv)m(en)h(b)m(y)e(the)h Fr(Hartr)-5 b(e)g(e)236 5336 y(e)g(quation)351 5581 y Fp(@)399 5595 y Fo(t)429 5581 y Fp( )488 5595 y Fo(t)518 5581 y Fw(\()p Fp(x)p Fw(\))51 b(=)g Fq(f)p Fl(H)27 b Fp(;)15 b( )1072 5595 y Fo(t)1102 5581 y Fw(\()p Fp(x)p Fw(\))q Fq(g)51 b Fw(=)f Fq(\000)p Fp(i)1544 5453 y Fm(\024)1592 5581 y Fq(\000)1713 5520 y Fw(1)p 1673 5561 126 4 v 1673 5644 a(2)p Fp(m)1808 5581 y Fw(\001)20 b(+)g Fp(V)g Fw(\()p Fp(x)p Fw(\))2191 5453 y Fm(\025)2239 5581 y Fp( )2298 5595 y Fo(t)2328 5581 y Fw(\()p Fp(x)p Fw(\))h Fq(\000)e Fp(i)2592 5508 y Fm(\000)2634 5581 y Fp(\036)i Fq(\003)f(j)p Fp( )2858 5595 y Fo(t)2889 5581 y Fq(j)2914 5544 y Fs(2)2953 5508 y Fm(\001)2995 5581 y Fw(\()p Fp(x)p Fw(\))15 b Fp( )3191 5595 y Fo(t)3222 5581 y Fw(\()p Fp(x)p Fw(\))g Fp(;)116 b Fw(\(45\))p Black 1903 5871 a(10)p Black eop end %%Page: 11 11 TeXDict begin 11 10 bop Black Black 236 162 a Fw(where)35 b Fq(\003)g Fw(denotes)g(con)m(v)m(olution;)40 b(\()p 1472 88 63 4 v Fp( )1534 184 y Fo(t)1564 162 y Fw(\()p Fp(x)p Fw(\))c(satis\014es)f(the)g(complex)h(conjugate)g(equation\).)55 b(Since)236 275 y Fp(V)g Fw(is)34 b(smo)s(oth)g(and)f(p)s(olynomially)i 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5320 y Fm(b)1037 5343 y Fp(A)1105 5357 y Fo(N)1174 5343 y Fw(\()p Fp(a)1257 5295 y Fs(\()p Fo(p)p Fs(\))1257 5367 y Fo(t)1351 5343 y Fw(\))1387 5270 y Fm(\003)1475 5343 y Fw(=)1644 5230 y Fs(2)1596 5257 y Fm(X)1606 5455 y Fo(l)q Fs(=1)1743 5215 y Fm(\022)1810 5282 y Fp(p)1818 5406 y(l)1856 5215 y Fm(\023)o(\022)1989 5282 y Fw(2)1998 5406 y Fp(l)2035 5215 y Fm(\023)2204 5282 y Fp(il)p 2112 5322 245 4 v 2112 5406 a Fw(2)p Fp(N)2240 5379 y Fo(l)q Fn(\000)p Fs(1)2403 5320 y Fm(b)2381 5343 y Fp(A)2449 5357 y Fo(N)2517 5270 y Fm(\000\002)2596 5343 y Fw(\()p Fp(\036)2685 5306 y Fs(\(2\))2685 5366 y Fo(s)2780 5343 y Fw(\))26 b Fp(*)2875 5405 y Fo(l)2972 5343 y Fw(\()p Fp(a)3055 5295 y Fs(\()p Fo(p)p Fs(\))3055 5367 y Fo(t)3150 5343 y Fw(\))3185 5270 y Fm(\003\001)3500 5343 y Fw(\(61\))p Black 1903 5871 a(12)p Black eop end %%Page: 13 13 TeXDict begin 13 12 bop Black Black 236 162 a Fw(suggests)40 b(splitting)g(the)f(iterated)i(series)e(in)m(to)h(t)m(w)m(o)h(parts.)67 b(As)39 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