Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heat Kernel Asymptotics, Path Integrals and Infinite-Dimensional
  Determinants   We investigate the short-time expansion of the heat kernel of a Laplace type
operator on a compact Riemannian manifold and show that the lowest order term
of this expansion is given by the Fredholm determinant of the Hessian of the
energy functional on a space of finite energy paths. This is the asymptotic
behavior to be expected from formally expressing the heat kernel as a path
integral and then (again formally) using Laplace's method on the integral. We
also relate this to the zeta determinant of the Jacobi operator, which is
another way to assign a determinant to the Hessian of the energy functional. We
consider both the near-diagonal asymptotics as well as the behavior at the cut
locus.

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The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph