Worldline Images for Yang-Mills Theory within Boundaries

TL;DR

This paper introduces a worldline method with the method of images to analyze Yang-Mills theories on manifolds with boundaries, including boundary conditions, heat kernel coefficients, and gluon production rates.

Contribution

It develops a novel worldline approach for Yang-Mills theories with boundaries, incorporating boundary conditions and calculating physical quantities.

Findings

Computed the first three Seeley-DeWitt coefficients for boundary heat kernels.

Calculated gluon production rates in chromoelectric fields with boundaries.

Validated the method through consistency checks.

Abstract

In this article we develop a worldline technique based on the method of images to study the effective action associated to Yang-Mills theories on manifolds with boundaries. We consider the possibility of having either relative or absolute boundary conditions, which are particular types of mixed boundary conditions. Both vector fields and ghost fields are taken into account in this analysis. As a check of our construction, we compute the first three Seeley-DeWitt coefficients of the heat kernel asymptotics. Finally, we employ our technique to calculate the rate of gluon production due to a chromoelectric field background in the presence of a boundary.