Confinement of quarks

TLDR

The structure resembles relativistic string models of hadrons. The paper defines a total quark confinement mechanism, akin to Schwinger’s, that requires Abelian or non‑Abelian gauge fields. The authors formulate the mechanism by quantizing gauge fields on a discrete Euclidean lattice with exact gauge invariance, treating fields as angular variables, and employing a strong‑coupling expansion over quark paths and lattice surfaces. In the strong‑coupling limit, the theory predicts confinement with no free quarks, but lacks Lorentz or Euclidean invariance.

Abstract

A mechanism for total confinement of quarks, similar to that of Schwinger, is defined which requires the existence of Abelian or non-Abelian gauge fields. It is shown how to quantize a gauge field theory on a discrete lattice in Euclidean space-time, preserving exact gauge invariance and treating the gauge fields as angular variables (which makes a gauge-fixing term unnecessary). The lattice gauge theory has a computable strong-coupling limit; in this limit the binding mechanism applies and there are no free quarks. There is unfortunately no Lorentz (or Euclidean) invariance in the strong-coupling limit. The strong-coupling expansion involves sums over all quark paths and sums over all surfaces (on the lattice) joining quark paths. This structure is reminiscent of relativistic string models of hadrons.