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Communications in Mathematical Physics 230 (2002) 245-269
Quasiclassical expansion for $Tr{(-1)^F ^{-\beta H}}$
A.V. Smilga1

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(-\beta H)} can be calculated at small \beta. 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 \beta^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.
1 :  SUBATECH - Laboratoire SUBATECH Nantes
Mathématiques/Physique mathématique

Physique/Physique mathématique

Physique/Physique des Hautes Energies - Théorie
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