# Path Integrals on Manifolds with Boundary

#### Autoren: Matthias Ludewig (2017)

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.

Zeitschrift:
Comm. Math. Phys.
Verlag:
Springer
Seiten:
621-640
Band:
354, no. 2

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