Perturbation theory for the two-dimensional abelian Higgs model in the unitary gauge

TL;DR

This paper investigates the perturbation theory of the two-dimensional abelian Higgs model in the unitary gauge, resolving conflicts with the R_xi gauge and demonstrating the consistency of physical results.

Contribution

It provides a detailed analysis of one-loop perturbation theory in the unitary gauge, clarifying its relation to the R_xi gauge and confirming the physical equivalence.

Findings

Resolved the apparent conflict between the unitary gauge and R_xi gauge limits.

Demonstrated that physical quantities can be reliably computed in the unitary gauge.

Showed the formal equivalence of the unitary gauge to the limit  of the R_xi gauge.

Abstract

In the unitary gauge the unphysical degrees of freedom of spontaneously broken gauge theories are eliminated. The Feynman rules are simpler than in other gauges, but it is non-renormalizable by the rules of power counting. On the other hand, it is formally equal to the limit $\xi \to 0$ of the renormalizable R$_{\xi}$-gauge. We consider perturbation theory to one-loop order in the R$_{\xi}$-gauge and in the unitary gauge for the case of the two-dimensional abelian Higgs model. An apparent conflict between the unitary gauge and the limit $\xi \to 0$ of the R$_{\xi}$-gauge is resolved, and it is demonstrated that results for physical quantities can be obtained in the unitary gauge.