Group averaging, positive definiteness and superselection sectors

TL;DR

This paper examines group averaging in quantizing constrained systems with noncompact gauge groups, analyzing convergence, inner product definiteness, and superselection sectors through three case studies.

Contribution

It provides new insights into the conditions for convergence and the structure of superselection sectors in noncompact gauge group quantization.

Findings

Convergence conditions for group averaging are identified.

Indefiniteness of the physical inner product can occur.

Superselection sectors naturally emerge in the studied cases.

Abstract

I discuss group averaging as a method for quantising constrained systems whose gauge group is a noncompact Lie group. Focussing on three case studies, I address the convergence of the averaging, possible indefiniteness of the prospective physical inner product and the emergence of superselection sectors.