• DOI:10.1007/s00220-009-0973-3
• Corpus ID: 14006237

Asymptotic Heat Kernel Expansion in the Semi-Classical Limit

@article{Br2008AsymptoticHK,
  title={Asymptotic Heat Kernel Expansion in the Semi-Classical Limit},
  author={Christian B{\"a}r and Frank Pf{\"a}ffle},
  journal={Communications in Mathematical Physics},
  year={2008},
  volume={294},
  pages={731-744}
}

• Christian Bär, Frank Pfäffle
• Published 6 May 2008
• Mathematics
• Communications in Mathematical Physics

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.