A Remark on Formal KMS States in Deformation Quantization

Details A Remark on Formal KMS States in Deformation Quantization A Remark on Formal KMS States in Deformation Quantization

1998-01-30

arxiv.org/abs/math/9801139v1

Lett.Math.Phys. 45 (1998) 49-61

Mathematics

Quantum Algebra

11 pages, LaTeX2e

Scientific paper

In the framework of deformation quantization we define formal KMS states on the deformed algebra of power series of functions with compact support in phase space as C[[\lambda]]-linear functionals obeying a formal variant of the usual KMS condition known in the theory of C^*-algebras. We show that for each temperature KMS states always exist and are up to a normalization equal to the trace of the argument multiplied by a formal analogue of the usual Boltzmann factor, a certain formal star exponential.

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