Communications in Mathematical Physics

, Volume 230, Issue 2, pp 245–269 | Cite as

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

  • A. V. Smilga


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 S3 and show that the quasiclassical expansion breaks down for this system.


Partition Function Quantum System Mechanical System Mill Theory Quantum Mechanical System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • A. V. Smilga
    • 1
  1. 1.SUBATECH, Université de Nantes, 4 rue Alfred Kastler, BP 20722, 44307 Nantes, FranceFR

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