Constant External Fields in Gauge Theory and the Spin 0, 1/2, 1 Path Integrals

TL;DR

This paper explores the application of the string-inspired worldline path integral method to gauge theory calculations involving constant external fields, providing detailed computations of effective actions for scalars, spinors, and gluons.

Contribution

It demonstrates how to incorporate external fields into the worldline formalism and calculates effective actions at one- and two-loop levels for different particle loops.

Findings

Derived explicit two-loop effective actions for scalar and spinor loops.

Reexamined the worldline representation of the gluon loop in external fields.

Extended the Bern-Kosower formalism to include constant external backgrounds.

Abstract

We investigate the usefulness of the "string-inspired technique" for gauge theory calculations in a constant external field background. Our approach is based on Strassler's worldline path integral approach to the Bern-Kosower formalism, and on the construction of worldline (super--) Green's functions incorporating external fields as well as internal propagators. The worldline path integral representation of the gluon loop is reexamined in detail. We calculate the two-loop effective actions induced for a constant external field by a scalar and spinor loop, and the corresponding one-loop effective action in the gluon loop case.