Polyakov Loop in Non-covariant Operator Formalism

TL;DR

This paper explores the formulation of the Polyakov loop within a non-covariant operator framework, linking it to the covariant formalism at finite temperature through physical degrees of freedom.

Contribution

It demonstrates how to express the Polyakov loop operator using only physical operators in non-covariant formalism, connecting it to the covariant path integral approach.

Findings

Polyakov loop can be represented in non-covariant operator formalism.

Vacuum expectation value matches covariant formalism in axial and Coulomb gauges.

Provides a bridge between operator and path integral formalisms at finite temperature.

Abstract

We discuss a Polyakov loop in non-covariant operator formalism which consists of only physical degrees of freedom at finite temperature. It is pointed out that although the Polyakov loop is expressed by a Euclidean time component of gauge fields in a covariant path integral formalism, there is no direct counterpart of the Polyakov loop operator in the operator formalism because the Euclidean time component of gauge fields is not a physical degree of freedom. We show that by starting with an operator which is constructed in terms of only physical operators in the non-covariant operator formalism, the vacuum expectation value of the operator calculated by trace formula can be rewritten into a familiar form of an expectation value of Polyakov loop in a covariant path integral formalism at finite temperature for the cases of axial and Coulomb gauge.