Quantization of diffeomorphism invariant theories of connections with local degrees of freedom

Abstract

Quantization of diffeomorphism invariant theories of connections is studied. A complete solution of the diffeomorphism constraints is found. The space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions. This provides, in particular, a quantization of the Husain-Kucha\\v{r} model. The main results also pave way to quantization of other diffeomorphism invariant theories such as general 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 combined in an appropriate fashion with a coherent state transform to incorporate complex connections.