The Gauss Law: A Tale

TL;DR

This paper surveys the role of Gauss law in gauge theories, discussing gauge invariance, edge states, superselection sectors, and spontaneous symmetry breaking in both abelian and nonabelian models.

Contribution

It provides a comprehensive review of Gauss law implications in various gauge theories and introduces reformulations of nonlinear G/H models as gauge theories.

Findings

Nonabelian superselection rules are spontaneously broken.

SU(3) color symmetry is spontaneously broken to U(1)×U(1).

Edge states and superselection sectors are established in reformulated models.

Abstract

The Gauss law plays a basic role in gauge theories, enforcing gauge invariance and creating edge states and superselection sectors. This article surveys these aspects of the Gauss law in QED, QCD and nonlinear $G/H$ models. It is argued that nonabelian superselection rules are spontaneously broken. That is the case with $SU(3)$ of colour which is spontaneously broken to $U(1)\times U(1)$. Nonlinear $G/H$ models are reformulated as gauge theories and the existence of edge states and superselection sectors in these models is also established.