Difficulties in Formulating an imaginary-time formalism of temporal axial gauge at finite T

TL;DR

This paper explores the challenges of developing an imaginary-time formalism in temporal axial gauge at finite temperature, highlighting fundamental issues with energy conservation that hinder its formulation.

Contribution

It critically examines the difficulties in extending the imaginary-time formalism in temporal axial gauge, revealing fundamental obstacles not present in the real-time approach.

Findings

Energy conservation fails in the imaginary-time formalism

Unusual representation of the longitudinal field causes issues

Formulation challenges hinder studying Debye screening in QCD

Abstract

Following the successful construction of the finite T real-time formalism in temporal axial gauge, we attempt to further study the equivalent new imaginary-time formalism of James and Landshoff based on the same Hamiltonian approach in the hope that it will provide the answer to Debye screening in QCD. It turns out that, unlike in the real-time case, energy conservation does not hold because of the unusual representation of the longitudinal field forced upon by the Hamiltonian formulation.