  This work addresses a specific technical question of relevance to canonical
quantization of gravity using the so-called new variables and loop-based
techniques of Ashtekar, Rovelli, and Smolin. In particular, certain
`superselection laws' that arise in current applications of these techniques to
solving the diffeomorphism constraint are considered. Their status is
elucidated by studying an analogous system: 2+1 Euclidean gravity. For that
system, these superselection laws are shown to be spurious. This, however, is
only a technical difficulty. The usual quantum theory may still be obtained
from a loop representation and the technique known as `Refined Algebraic
Quantization.'
