Gauge Invariant States of QCD

TL;DR

This paper introduces new gauge-invariant states in QCD that are exact solutions to the Dirac condition, overcoming non-perturbative gauge invariance issues caused by Gribov copies, and are constructed in coordinate space.

Contribution

The paper presents a novel construction of gauge-invariant QCD states that are exact solutions to the Dirac condition, valid non-perturbatively and defined in coordinate space.

Findings

States are gauge invariant non-perturbatively.

States are restricted to meson-like, baryon-like, or anti-baryon-like configurations.

Use of coordinate space creation operators distinguishes these states.

Abstract

None of the asymptotic states commonly used in perturbative QCD are gauge invariant. A similar statement could be made about QED, but in QED one can construct gauge invariant "dressed" states (with Dirac electrons) that are unitarily equivalent to the states used in perturbation theory. Perturbative expansions of dressed states have been derived for QCD, but Gribov copies obstruct these states from remaining gauge invariant non-perturbatively. Introduced here are new QCD states that are exact solutions to the Dirac condition, so they remain gauge invariant non-perturbatively. The quark content of these states is restricted to be meson-like, baryon-like, or anti-baryon-like locally at each point of space. The states differ from others previously presented due to the use of creation operators defined in coordinate space rather than in momentum space.