Obtaining gluon propagator in a new generalized gauge

TL;DR

This paper introduces a new generalized gauge condition for quantizing gauge theories, deriving gluon propagators within this framework, which bridges existing covariant and non-covariant gauges and offers fresh insights into Yang-Mills theories.

Contribution

A novel generalized gauge condition is proposed, enabling derivation of gluon propagators that unify covariant and non-covariant gauge results within the path integral formalism.

Findings

Derived gluon propagators in the new gauge

Reproduced known propagators in specific limit cases

Provided a new perspective on gauge fixing in QFT

Abstract

Gauge theories play a fundamental role in particle physics, nuclear physics, and cosmology. The basic idea of these theories is that the Lagrangian density should be invariant under some transformations. Lagrangian invariance implies a certain freedom in defining gauge fields. In this study, the standard path integral quantization formalism is used. Gauge degrees of freedom manifest themselves in the difficulties in obtaining gauge field propagators. For a consistent quantization, it is necessary to eliminate non-physical gauge degrees of freedom. The standard procedure is to break the gauge symmetry by applying a gauge condition. In this work, we introduced a new generalized gauge condition $W_{\mu} A^{a\mu}=0$, where $W_{\mu}=\lambda \partial_{\mu}+\beta n_{\mu}$, $n_{\mu}$ is an arbitrary constant four-vector, $\lambda$, and $\beta$ are real constant parameters. Using standard path integral quantization formalism, we obtained gluon propagators expressions in this new gauge. In the $\lambda=1,\beta\rightarrow0$, and $\beta=1, \lambda\rightarrow0$ limit cases, the obtained expression provides us the gluon propagators expressions available in the literature in covariant and non-covariant gauges, respectively. This study can give us a different perspective on quantization in Yang-Mills (YM) theories and can show the way to some ambiguities in quantum field theories (QFT).