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arXiv · hep-th/0110105

Quasiclassical expansion for Tr{(-1)^F exp(-βH)}

A. V. Smilga
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Abstract

We start with some methodic remarks referring to purely bosonic quantum systems and then explain how corrections to the leading--order quasiclassical result for the fermion--graded partition function Tr{(-1)^F exp(-βH)} can be calculated at small β. We perform such calculation for certain supersymmetric quantum mechanical systems where such corrections are expected to appear. We consider in particular supersymmetric Yang-Mills theory reduced to (0+1) dimensions and were surprised to find that the correction of order β^2 vanishes in this case. We discuss also a nonstandard N =2 supersymmetric sigma model defined on S^3 and other 3--dimensional conformally flat manifolds and show that the quasiclassical expansion breaks down for this system.

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A. V. Smilga. 2002-02-07. Quasiclassical expansion for Tr{(-1)^F exp(-βH)}. https://doi.org/10.1007/s00220-002-0673-8

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