Rigorous three-dimensional relativistic equation for quark-antiquark bound states at finite temperature derived from the thermal QCD formulated in the coherent-state representation

TL;DR

This paper derives a rigorous three-dimensional relativistic equation for quark-antiquark bound states at finite temperature from thermal QCD, providing a new path-integral formulation and a kernel suitable for studying quark deconfinement.

Contribution

It introduces a novel derivation of the three-dimensional relativistic equation from thermal QCD using the coherent-state path integral and provides a closed-form interaction kernel.

Findings

Derived a new generating functional with a correct path-integral expression.

Presented a closed-form interaction kernel based on equations of motion.

Applied the framework to derive the one-gluon exchange kernel.

Abstract

A rigorous three-dimensional relativistic equation for quark-antiquark bound states at finite temperature is derived from the thermal QCD generating functional which is formulated in the coherent-state representation. The generating functional is derived newly and given a correct path-integral expression. The perturbative expansion of the generating functional is specifically given by means of the stationary-phase method. Especially, the interaction kernel in the three-dimensional equation is derived by virtue of the equations of motion satisfied by some quark-antiquark Green functions and given in a closed form which is expressed in terms of only a few types of Green functions. This kernel is much suitable to use for exploring the deconfinement of quarks. To demonstrate the applicability of the equation derived, the one-gluon exchange kernel is derived and described in detail.