Quantum modular group in (2+1)-dimensional gravity - art. no. 024012

The role of the modular group in the holonomy representation of (2 + 1)-dim ensional quantum gravity is studied. This representation can be viewed as a "Heisenberg picture," and for simple topologies, the transformation to the ADM "Schrodinger picture" may be found. For spacetimes with the spatial to pology of a torus. this transformation and an explicit operator representat ion of the mapping class group are constructed. It is shown that the quantu m modular group splits the holonomy representation Hilbert space into physi cally equivalent orthogonal ''fundamental regions" that are interchanged by modular transformations. [S0556-2821(99)02302-4].