Non-Quadratic Gauge Fixing and Global Gauge Invariance in the Effective Action

TL;DR

This paper introduces a non-quadratic gauge fixing method in effective actions for gauge theories, maintaining global gauge invariance and avoiding quadratic scalar terms, with implications for ghost fields and propagator properties.

Contribution

It presents a novel non-quadratic gauge fixing approach in effective actions, applicable to spin-two and spontaneously broken gauge theories, preserving global gauge invariance.

Findings

Enables traceless and transverse propagators in spin-two theories

Avoids quadratic scalar terms in gauge fixing for broken gauge theories

Introduces a consistent ghost field structure with global invariance

Abstract

The possibility of having a gauge fixing term in the effective Lagrangian that is not a quadratic expression has been explored in spin-two theories so as to have a propagator that is both traceless and transverse. We first show how this same approach can be used in spontaneously broken gauge theories as an alternate to the 't Hooft gauge fixing which avoids terms quadratic in the scalar fields. This "non-quadratic" gauge fixing in the effective action results in there being two complex Fermionic and one real Bosonic ghost fields. A global gauge invariance involving a Fermionic gauge parameter, analogous to the usual BRST invariance, is present in this effective action.