On Group Averaging for SO(n,1)

TL;DR

This paper explores a 'renormalized' group averaging method for constrained systems, examining its applicability and potential links to superselection sectors and divergence rates in specific models.

Contribution

It introduces a renormalized approach to group averaging and investigates its connection to superselection sectors and divergence behavior.

Findings

Renormalized group averaging can be well-defined in certain models.

Potential link between superselection sectors and divergence rates.

Provides insights into the limitations of standard group averaging.

Abstract

The technique known as group averaging provides powerful machinery for the study of constrained systems. However, it is likely to be well defined only in a limited set of cases. Here, we investigate the possibility of using a `renormalized' group averaging in certain models. The results of our study may indicate a general connection between superselection sectors and the rate of divergence of the group averaging integral.