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Type: Journal article
Title: Heat kernel asymptotics, path integrals and infinite-dimensional determinants
Author: Ludewig, M.
Citation: Journal of Geometry and Physics, 2018; 131:66-88
Publisher: Elsevier
Issue Date: 2018
ISSN: 0393-0440
Statement of
Matthias Ludewig
Abstract: We compare the short-time expansion of the heat kernel on a Riemannian manifold with the formal stationary phase expansion of its representing path integral and prove that these asymptotic expansions coincide. Besides shedding light on the formal properties of quantum mechanical path integrals, this shows that the lowest order term of the heat kernel expansion is given by the Fredholm determinant of the Hessian of the energy functional on the space of finite energy paths. We also relate this to the zeta determinant of the Jacobi operator, considering both the near-diagonal asymptotics as well as the behavior at the cut locus.
Keywords: Path integrals; heat kernels; heat kernel asymptotics; Fredholm determinant; zeta function; zeta determinant
Rights: © 2018 Elsevier B.V. All rights reserved.
DOI: 10.1016/j.geomphys.2018.04.012
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Appears in Collections:Aurora harvest 3
Mathematical Sciences publications

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