Massive quantum fields in a conical background

TL;DR

This paper derives Klein-Gordon and Dirac propagators in a conical background, revealing their relation to the Aharonov-Bohm effect and proposing extensions to arbitrary spin fields.

Contribution

It provides explicit representations of propagators for massive quantum fields in conical geometries, including a novel relation between Dirac and Klein-Gordon propagators.

Findings

Propagators expressed in conical backgrounds for massive fields.

Relation between Dirac and Klein-Gordon propagators involving cone deficit angles.

Analogies with the Aharonov-Bohm effect and a conjecture for arbitrary spin fields.

Abstract

Representations of the Klein-Gordon and Dirac propagators are determined in a $N$ dimensional conical background for massive fields twisted by an arbitrary angle $2\pi\sigma$. The Dirac propagator is shown to be obtained from the Klein-Gordon propagator twisted by angles $2\pi\sigma\pm {\cal D}/2$ where ${\cal D}$ is the cone deficit angle. Vacuum expectation values are determined by a point-splitting method in the proper time representation of the propagators. Analogies with the Aharonov-Bohm effect are pointed out throughout the paper and a conjecture on an extension to fields of arbitrary spin is given.