Communications in Mathematical Physics

, Volume 294, Issue 3, pp 731–744 | Cite as

Asymptotic Heat Kernel Expansion in the Semi-Classical Limit

  • Christian BärEmail author
  • Frank Pfäffle


Let \({H_\hbar = \hbar^{2}L +V}\), where L is a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold and V is a symmetric endomorphism field. We derive an asymptotic expansion for the heat kernel of \({H_\hbar}\) as \({\hbar \searrow 0}\). As a consequence we get an asymptotic expansion for the quantum partition function and we see that it is asymptotic to the classical partition function. Moreover, we show how to bound the quantum partition function for positive \({\hbar}\) by the classical partition function.


Partition Function Asymptotic Expansion Dirac Operator Heat Kernel Compact Riemannian Manifold 
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© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Universität Potsdam, Institut für MathematikPotsdamGermany

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