 06145 Detlev Buchholz, Hendrik Grundling
 Algebraic Supersymmetry: A case study
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May 2, 06

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Abstract. The treatment of supersymmetry is known to cause
difficulties in the C*algebraic framework of relativistic quantum field theory; several nogo theorems indicate that superderivations and superKMS functionals must be quite singular objects in a C*algebraic setting. In order to clarify the situation,
a simple supersymmetric chiral field theory
of a free Fermi and Bose field defined on R is analyzed. It is shown that a meaningful C*version of this model can be based on the tensor
product of a CARalgebra and a novel version of a
CCRalgebra, the "resolvent algebra".
The elements of this resolvent algebra serve as
mollifiers for the superderivation. Within this model, unbounded
(yet locally bounded) graded KMSfunctionals are constructed and
proven to be supersymmetric. From these KMSfunctionals, Chern
characters are obtained by generalizing formulae of Kastler and
of Jaffe, Lesniewski and Osterwalder. The characters are used to
define cyclic cocycles in the sense of Connes' noncommutative geometry which are ``locally entire''.
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