Perturbative Analysis of Chern-Simons Field Theory in the Coulomb Gauge

TL;DR

This paper investigates the perturbative properties of Chern-Simons field theory in the Coulomb gauge, demonstrating the absence of divergences and radiative corrections, and addressing gauge fixing issues with a regularization method applicable to Yang-Mills theories.

Contribution

It provides a detailed perturbative analysis showing zero radiative corrections and introduces a regularization technique for spurious singularities in Coulomb gauge.

Findings

No ultraviolet or infrared divergences in perturbative expansion.

All radiative corrections are zero at any loop order.

Regularization method applicable to Yang-Mills theories.

Abstract

In this paper we analyse the perturbative aspects of Chern-Simons field theories in the Coulomb gauge. We show that in the perturbative expansion of the Green functions there are neither ultraviolet not infrared divergences. Moreover, all the radiative corrections are zero at any loop order. Some problems connected with the Coulomb gauge fixing, like the appearance of spurious singularities in the computation of the Feynman diagrams, are discussed and solved. The regularization used here for the spurious singularities can be easily applied also to the Yang-Mills case, which is affected by similar divergences.