Worldline Approach to QFT on Manifolds with Boundary
F. Bastianelli, O. Corradini, P. A. G. Pisani, C. Schubert
TL;DR
This paper develops a worldline path integral method to compute the heat kernel trace for scalar fields on manifolds with boundaries, providing new formulas and discussing potential extensions.
Contribution
It introduces a non-iterative worldline approach to evaluate heat kernel traces with boundary conditions, advancing computational techniques in quantum field theory.
Findings
Derived master formulas for heat kernel trace with boundary conditions
Presented a worldline path integral representation for scalar fields
Discussed potential extensions of the method
Abstract
We use the image charge method to compute the trace of the heat kernel for a scalar field on a flat manifold with boundary, representing the trace by means of a worldline path integral and obtain useful non-iterative master formulae for n insertions of the scalar potential. We discuss possible extensions of the method.
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