Asymptotic heat kernel expansion in the semi-classical limit

Details Asymptotic heat kernel expansion in the semi-classical limit Asymptotic heat kernel expansion in the semi-classical limit

2008-05-06

arxiv.org/abs/0805.0704v3

Commun. Math. Phys. 294 (2010), 731-744

Physics

Mathematical Physics

Minor changes, published version

Scientific paper

10.1007/s00220-009-0973-3

Let $H_h = h^2 L +V$ 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 $H_h$ as $h \to 0$. 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 $h$ by the classical partition function.

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