Form Invariance, Topological Fluctuations and Mass Gap of Yang-Mills Theory

TL;DR

This paper explores the quantum Yang-Mills theory with topologically nontrivial backgrounds, revealing how topological fluctuations and form invariance conditions contribute to the emergence of a mass gap, akin to the Higgs mechanism.

Contribution

It introduces a novel approach by constraining gauge fields with form invariance and topological properties, leading to classical solutions and quantum fluctuations that generate a mass gap.

Findings

Classical solutions are recovered under constraints.

Topological fluctuations form the quantum background.

A mass gap emerges at semi-classical level.

Abstract

In order to have a new perspective on the long-standing problem of the mass gap in Yang-Mills theory, we study the quantum Yang-Mills theory in the presence of topologically nontrivial backgrounds in this paper. The topologically stable gauge fields are constrained by the form invariance condition and the topological properties. Obeying these constraints, the known classical solutions to the Yang-Mills equation in the 3- and 4-dimensional Euclidean spaces are recovered, and the other allowed configurations form the nontrivial topological fluctuations at quantum level. Together, they constitute the background configurations, upon which the quantum Yang-Mills theory can be constructed. We demonstrate that the theory mimics the Higgs mechanism in a certain limit and develops a mass gap at semi-classical level on a flat space with finite size or on a sphere.