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 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.
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Received: 12 December 2001 / Accepted: 29 January 2002¶Published online: 11 September 2002
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Smilga, A. Quasiclassical Expansion for Tr { (−1)F e − β H}. Commun. Math. Phys. 230, 245–269 (2002). https://doi.org/10.1007/s00220-002-0673-8
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DOI: https://doi.org/10.1007/s00220-002-0673-8