CANONICAL QUANTUM SUPERGRAVITY IN 3 DIMENSIONS

We discuss the canonical treatment and quantization of matter coupled supergravity in three dimensions, with special emphasis on N = 2 super gravity. We then analyze the quantum constraint algebra; certain opera tor ordering ambiguities are found to be absent due to local supersymm etry. We show that the supersymmetry constraints can be partially solv ed by a functional analog of the method of characteristics. We also co nsider extensions of Wilson loop integrals of the type previously foun d in ordinary gravity, but now with connections involving the bosonic and fermionic matter fields in addition to the gravitational connectio n. In a separate section of this paper, the canonical treatment and qu antization of non-linear coset space sigma models are discussed in a s elf-contained way.