Renormalization in Coulomb-gauge QCD within the Lagrangian formalism

TL;DR

This paper proves the algebraic renormalizability of Coulomb-gauge QCD using the Lagrangian formalism, deriving key identities and analyzing the invariance of specific propagator components under renormalization.

Contribution

It provides a rigorous proof of renormalizability for Coulomb-gauge QCD within the Lagrangian second-order formalism, including the derivation of Ward and Zinn-Justin identities.

Findings

Algebraic renormalizability of Coulomb-gauge QCD established.

g^2D^{00} remains invariant under renormalization.

Derived Ward identity and Zinn-Justin equation for the theory.

Abstract

We study renormalization of Coulomb-gauge QCD within the Lagrangian second-order formalism. We derive a Ward identity and the Zinn-Justin equation, and, with the help of the latter, we give a proof of algebraic renormalizability of the theory. Through diagrammatic analyses, we show that, in the strict Coulomb gauge, g^2D^{00} is invariant under renormalization. (D^{00} is the time-time component of the gluon propagator.)