MODULAR GROUP, OPERATOR ORDERING, AND TIME IN (2-DIMENSIONAL GRAVITY(1))

A choice of time slicing in classical general relativity permits the c onstruction of time-dependent wave functions in the ''frozen time'' Ch ern-Simons formulation of (2 + 1)-dimensional quantum gravity. Because of operator-ordering ambiguities, however, these wave functions are n ot unique. It is shown that when space has the topology of a torus, su itable operator orderings give rise to wave functions that transform u nder the modular group as automorphic functions of arbitrary weights, with dynamics determined by the corresponding Maass Laplacians on modu li space.