Phys. Rev. D 47, 4520–4524 (1993)Modular group, operator ordering, and time in (2+1)-dimensional gravityReceived 20 January 1993; published in the issue dated 15 May 1993 A choice of time slicing in classical general relativity permits the construction of time-dependent wave functions in the "frozen time" Chern-Simons formulation (2 + 1)-dimensional quantum gravity. Because of operator-ordering ambiguities, however, these wave functions are not unique. It is shown that when space has the topology of a torus, suitable operator orderings give rise to wave functions that transform under the modular group as automorphic functions of arbitrary weights, with dynamics determined by the corresponding Maass Laplacians on moduli space. © 1993 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.47.4520
DOI:
10.1103/PhysRevD.47.4520
PACS:
04.60.+n
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