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.Comment: Minor corrections, 17 pages,RevTe
