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arXiv · 1607.05151

Path Integrals on Manifolds with Boundary

Matthias Ludewig
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Abstract

We give time-slicing path integral formulas for solutions to the heat equation corresponding to a self-adjoint Laplace type operator acting on sections of a vector bundle over a compact Riemannian manifold with boundary. More specifically, we show that such a solution can be approximated by integrals over finite-dimensional path spaces of piecewise geodesics subordinated to increasingly fine partitions of the time interval. We consider a subclass of mixed boundary conditions which includes standard Dirichlet and Neumann boundary conditions.

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Matthias Ludewig. 2016-07-18. Path Integrals on Manifolds with Boundary. https://doi.org/10.1007/s00220-017-2915-9

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