Bulg. J. Phys. vol.35 no.s1 (2008), pp. 316-322

Supersymmetry in Thermal Background - Reconstruction Theory

Orlin Stoytchev1,2
1American University in Bulgaria, 2700 Blagoevgrad, Bulgaria
2Institute for Nuclear Research, 1784 Sofia, Bulgaria
Abstract. An algebraic supersymmetric quantum field theory in a thermal background is supposed to provide the following data - a Z2-graded C*-dynamical system, a (possibly unbounded) self-adjoint graded-KMS functional on it and a superderivation of the algebra (the supersymmetry generator), whose square is the generator of the evolution group. It is shown how one can reconstruct canonically from this data a representation of the theory in a Z2-graded Hilbert space, so that the grading of the Hilbert space is in some natural way compatible with the functional. The superderivation is implemented as a graded commutator with an unbounded odd operator (supercharge). The modular conjugation operator plays a crucial role in this reconstruction.

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