THETA-states induced by the diffeomorphism group in canonically quantized gravity

Studies of the effects of spatial or spacetime topology in quantum gravity seem to be a natural prerequisite to the quantization of the topology itself. The approach to the problem considered is the development of an analogue of the vacuum theta-structure that arises in Yang-Mills theory. The theta-and n-vacua of Yang-Mills theory are introduced via the configuration space and are shown to be equivalent to those obtained by more conventional means. The analogous treatment of canonically quantized gravity is discussed and some specific examples of disconnected diffeomorphism groups are given. Gravitational analogues of instantons and tunnelling are discussed. (U.K.)