Four Dimensional Quantum Yang-Mills Theory for Weak Coupling Strength: Mass Gap Implies Quark Confinement

TL;DR

This paper establishes that in 3+1 dimensional quantum Yang-Mills theory, quark confinement occurs at weak coupling if a mass gap exists, by extending Wilson loop analysis and Elitzur's theorem.

Contribution

It introduces a framework linking mass gap existence to quark confinement in Yang-Mills theory at weak coupling, extending previous theoretical results.

Findings

Quark confinement is proven for small coupling constants.

Extension of Elitzur's theorem to 3+1 dimensions.

Wilson loop analysis supports confinement at weak coupling.

Abstract

For the quantized Yang-Mills $3+1$ dimensional problem we introduce the Wilson loop, prove an extension of Elitzur's theorem and shown quark confinement for sufficiently small values of the bare coupling constant, provided the existence of the mass gap.