Resummed effective action in the world-line formalism

TL;DR

This paper develops a resummation technique for the scalar one-loop effective action using the world-line formalism, introducing an alternative scheme and discussing its applications to gauge fields.

Contribution

It presents a new resummation scheme based on the world-line formalism, simplifying calculations of the effective action and extending to gauge field applications.

Findings

Reproduces known results efficiently

Introduces a center of mass based resummation scheme

Applicable to gauge field effective actions

Abstract

Using the world-line method we resum the scalar one-loop effective action. This is based on an exact expression for the one-loop action obtained for a background potential and a Taylor expansion of the potential up to quadratic order in x-space. We thus reproduce results of Masso and Rota very economically. An alternative resummation scheme is suggested using ``center of mass'' based loops which is equivalent under the assumption of vanishing third and higher derivatives in the Taylor expansion but leads to simplified expressions. In an appendix some general issues concerning the relation between world-line integrals with fixed end points versus integrals with fixed center are clarified. We finally note that this method is also very valuable for gauge field effective actions where it is based on the Euler--Heisenberg type resummation.