THE STATUS OF DIFFEOMORPHISM SUPERSELECTION IN EUCLIDEAN 2-GRAVITY(1)

This work addresses a specific technical question of relevance to cano nical quantization of gravity using the so-called new variables and lo op-based techniques of Ashtekar, Rovelli, and Smolin. In particular, c ertain ''superselection laws'' that arise in current applications of t hese techniques to solving the diffeomorphism constraint are considere d, Their status is elucidated by studying an analogous system: 2 + 1 E uclidean gravity, For that system, these superselection laws are shown to be spurious. This, however, is only a technical difficulty. The us ual quantum theory may still be obtained from a loop representation an d the technique known as ''Refined Algebraic Quantization.'' (C) 1997 American Institute of Physics.