Gauss's law, gauge invariance, and long-range forces in QCD

TL;DR

This paper reformulates QCD Hamiltonian in a gauge-invariant way, revealing long-range interactions between color charges that could shed light on quark confinement and low-energy phenomena.

Contribution

It introduces a unitary transformation that makes the quark field gauge-invariant and replaces local gauge interactions with non-local long-range color charge interactions.

Findings

Long-range non-local interactions connect color charge densities.

Interactions between gauge-dependent parts are transformed away.

Implications for quark confinement are discussed.

Abstract

We use a unitary operator constructed in earlier work to transform the Hamiltonian for QCD in the temporal ($A_0=0$) gauge into a representation in which the quark field is gauge-invariant, and its elementary excitations -- quark and antiquark creation and annihilation operators -- implement Gauss's law. In that representation, the interactions between gauge-dependent parts of the gauge field and the spinor (quark) field have been transformed away and replaced by long-range non-local interactions of quark color charge densities. These long-range interactions connect SU(3) color charge densities through an infinite chain of gauge-invariant gauge fields either to other SU(3) color charge densities, or to a gluon "anchor". We discuss possible implications of this formalism for low-energy processes, including confinement of quarks that are not in color singlet configurations.