The ice-limit of Coulomb gauge Yang-Mills theory

TL;DR

This paper introduces a gauge-invariant framework for constructing multi-quark states in Coulomb gauge Yang-Mills theory, avoiding the Gribov problem and enabling clear analysis of the quark-antiquark potential.

Contribution

It develops an analytical 'ice-limit' approach to construct gauge-invariant states, extending the path integral framework and addressing the Gribov ambiguity.

Findings

Successfully constructs gauge-invariant mesonic states

Simulates the static quark-antiquark potential within this framework

Provides an unambiguous method to analyze confinement phenomena

Abstract

In this paper we describe gauge invariant multi-quark states generalising the path integral framework developed by Parrinello, Jona-Lasinio and Zwanziger to amend the Faddeev-Popov approach. This allows us to produce states such that, in a limit which we call the ice-limit, fermions are dressed with glue exclusively from the fundamental modular region associated with Coulomb gauge. The limit can be taken analytically without difficulties, avoiding the Gribov problem. This is llustrated by an unambiguous construction of gauge invariant mesonic states for which we simulate the static quark--antiquark potential.