Perturbative Computation of the Gluonic Effective Action via Polyaokov's World-Line Path Integral

TL;DR

This paper develops a perturbative method using Polyakov's world-line path integral to compute divergent terms of the gluonic effective action at one-loop order, simplifying the calculation by integrating over Grassmann and Feynman parameters.

Contribution

It introduces a novel approach employing the world-line path integral framework for gluonic effective action calculations, streamlining the process at one-loop order.

Findings

Successfully computed divergent terms to fourth order in perturbation theory.

Reduced complex Feynman diagram calculations to two integrations.

Demonstrated the method's efficiency in handling gluonic loop computations.

Abstract

The Polyakov world-line path integral describing the propagation of gluon field quanta is constructed by employing the background gauge fixing method and is subsequently applied to analytically compute the divergent terms of the one (gluonic) loop effective action to fourth order in perturbation theory. The merits of the proposed approach is that, to a given order, it reduces to performing two integrations, one over a set of Grassmann and one over a set of Feynman-type parameters through which one manages to accomodate all Feynman diagrams entering the computation at once.