Gauge-invariant description of Higgs phenomenon and quark confinement

TL;DR

This paper introduces a gauge-invariant framework for understanding the Higgs mechanism and quark confinement, avoiding assumptions of spontaneous symmetry breaking, and offers new insights into the confinement-Higgs relationship.

Contribution

It presents a gauge-invariant operator-level description of the Higgs mechanism that does not rely on spontaneous symmetry breaking, providing a new perspective on confinement-Higgs complementarity.

Findings

Gauge-invariant description of the Higgs mechanism at the operator level

Reinterpretation of Abelian dominance as gauge-invariant Higgs phenomenon

New perspective on the confinement-Higgs complementarity

Abstract

We propose a novel description for the Higgs mechanism by which a gauge boson acquires the mass. We do not assume spontaneous breakdown of gauge symmetry signaled by a non-vanishing vacuum expectation value of the scalar field. In fact, we give a manifestly gauge-invariant description of the Higgs mechanism in the operator level, which does not rely on spontaneous symmetry breaking. This enables us to discuss the confinement-Higgs complementarity from a new perspective. The "Abelian" dominance in quark confinement of the Yang-Mills theory is understood as a consequence of the gauge-invariant Higgs phenomenon for the relevant Yang-Mills-Higgs model.