Quasiclassical Expansion for Tr { (−1) F e − β H }

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 e ^{− β H} } can be calculated at small β. We perform such a 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 ∝ β² vanishes in this case. We discuss also a nonstandard N=2 supersymmetric σ-model defined on S ³ and show that the quasiclassical expansion breaks down for this system. Received: 12 December 2001 / Accepted: 29 January 2002?Published online: 11 September 2002