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The Status of Diffeomorphism Superselection in Euclidean 2+1 Gravity

Donald Marolf·José Mourão·Thomas Thiemann
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Abstract

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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Donald Marolf, José Mourão, Thomas Thiemann. 1997-01-30. The Status of Diffeomorphism Superselection in Euclidean 2+1 Gravity. https://doi.org/10.1063/1.532118

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