QUANTIZATION OF DIFFEOMORPHISM INVARIANT THEORIES OF CONNECTIONS WITHLOCAL DEGREES OF FREEDOM

Quantization of diffeomorphism invariant theories of connections is st udied and the quantum diffeomorphism constraint is solved. The space o f solutions is equipped with an inner product that is shown to satisfy the physical reality conditions. This provides, in particular, a quan tization of the Husain-Kuchar model. The main results also pave the wa y to quantization of other diffeomorphism invariant theories such as g eneral relativity. In the Riemannian case (i.e., signature ++++), the approach appears to contain all the necessary ingredients already. In the Lorentzian case, it will have to be combined in an appropriate fas hion with a coherent state transform to incorporate complex connection s. (C) 1995 American Institute of Physics.