Noncommutative U(1) gauge theory from a worldline perspective

TL;DR

This paper analyzes the one-loop effective action of noncommutative U(1) gauge theory using a phase space worldline path integral, highlighting renormalization and the separation of planar and non-planar contributions.

Contribution

It introduces a worldline formalism for noncommutative gauge theories that simplifies calculations and clarifies UV divergence structures.

Findings

Effective action calculation is independent of the worldline Green's function choice.

The formalism efficiently separates planar and non-planar contributions.

Homogeneous string-inspired Feynman rules simplify computations.

Abstract

We study pure noncommutative U(1) gauge theory representing its one-loop effective action in terms of a phase space worldline path integral. We write the quadratic action using the background field method to keep explicit gauge invariance, and then employ the worldline formalism to write the one-loop effective action, singling out UV-divergent parts and finite (planar and non-planar) parts, and study renormalization properties of the theory. This amounts to employ worldline Feynman rules for the phase space path integral, that nicely incorporate the Fadeev-Popov ghost contribution and efficiently separate planar and non-planar contributions. We also show that the effective action calculation is independent of the choice of the worldline Green's function, that corresponds to a particular way of factoring out a particle zero-mode. This allows to employ homogeneous string-inspired Feynman rules that greatly simplify the computation.