Gauge-independent Higgs mechanism and the implications for quark confinement

TL;DR

This paper presents a gauge-invariant framework for the Higgs mechanism that does not depend on spontaneous symmetry breaking, offering new insights into gauge boson mass generation and quark confinement.

Contribution

It introduces a gauge-invariant operator-level description of the Higgs mechanism, challenging the traditional reliance on spontaneous symmetry breaking.

Findings

Gauge-invariant description of the Higgs mechanism in $U(1)$ and $SU(2)$ models.

New perspective on the confinement-Higgs complementarity.

Potential implications for understanding quark confinement mechanisms.

Abstract

We propose a gauge-invariant description for the Higgs mechanism by which a gauge boson acquires the mass. We do not need to 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. For concreteness, we discuss the gauge-Higgs models with $U(1)$ and $SU(2)$ gauge groups explicitly. This enables us to discuss the confinement-Higgs complementarity from a new perspective.