LARGE DIFFEOMORPHISMS AND DIRAC QUANTIZATION OF CONSTRAINED SYSTEMS

Quantum dynamics of the flat toroidal n-geometry, based on the Einstein-Hilbert action with cosmological constant, is studied. The toroidal sectors of (2 + 1)-dimensional gravity and of Bianchi type I cosmology of general relativity are special cases of this model. The existence of proper large diffeomorphisms (LD) is shown in general as well as for the sub-model of diagonal toroidal metrics. In spite of this, the sub-model has a simply connected configuration space. Dirac quantization method is completed by a requirement of gauge invariance with respect to the LD. The corresponding unitary dynamics (theta sectors) are explicitly constructed for LAMBDA = 0 diagonal sub-models of dimensions two and three. The method is based on self-adjoint extensions of relevant operators over the fundamental domain of the LD.