The Status of Diffeomorphism Superselection in Euclidean 2+1 Gravity

Details The Status of Diffeomorphism Superselection in Euclidean 2+1 Gravity The Status of Diffeomorphism Superselection in Euclidean 2+1 Gravity

1997-01-30

arxiv.org/abs/gr-qc/9701068v1

J.Math.Phys. 38 (1997) 4730-4740

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Latex, 14 pages, to appear in Journ. Math. Phys

Scientific paper

10.1063/1.532118

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.'

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