Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1998-07-31
Phys.Rev.D59:024012,1999
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
23 pages, LaTeX, no figures; minor changes and clarifications in response to referee (basic argument and conclusions unaffecte
Scientific paper
10.1103/PhysRevD.59.024012
The role of the modular group in the holonomy representation of (2+1)-dimensional quantum gravity is studied. This representation can be viewed as a "Heisenberg picture", and for simple topologies, the transformation to the ADM "Schr{\"o}dinger picture" may be found. For spacetimes with the spatial topology of a torus, this transformation and an explicit operator representation of the mapping class group are constructed. It is shown that the quantum modular group splits the holonomy representation Hilbert space into physically equivalent orthogonal ``fundamental regions'' that are interchanged by modular transformations.
Carlip Steven
Nelson Jerry E.
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