Lattice Coulomb Hamiltonian and Static Color-Coulomb Field

TL;DR

This paper derives a lattice Coulomb-gauge Hamiltonian from Wilson's lattice gauge theory, incorporating a horizon function to enforce the fundamental modular region, and explores its implications for confinement and hadronic mass scale.

Contribution

It introduces an effective lattice Coulomb-gauge Hamiltonian with a horizon function to implement the fundamental modular region, linking the horizon condition to confinement.

Findings

The Hamiltonian satisfies lattice Gauss's law exactly.

The horizon condition determines the low-momentum ghost propagator behavior.

A confinement-like feature emerges in a weak-coupling expansion.

Abstract

The lattice Coulomb-gauge hamiltonian is derived from the transfer matrix of Wilson's Euclidean lattice gauge theory, wherein the lattice form of Gauss's law is satisfied identically. The restriction to a fundamental modular region (no Gribov copies) is implemented in an effective hamiltonian by the addition of a "horizon function" $G$ to the lattice Coulomb-gauge hamiltonian. Its coefficient $\gamma_0$ is a thermodynamic parameter that ultimately sets the scale for hadronic mass, and which is related to the bare coupling constant $g_0$ by a "horizon condition". This condition determines the low-momentum behavior of the (ghost) propagator that transmits the instantaneous longitudinal color-electric field, and thereby provides for a confinement-like feature in leading order in a new weak-coupling expansion.