Gravity based on Generalized Canonical Formalism

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The purpose of this reserach project is to study quantization of systems with local gauge invarinace such as gravitational theories and string theories on the basis of the generalized hamiltonian formalism developed by Batalin-Fradikin-Vilkoviski. In the last two years for term of the project, we have been carried out quantization of two-dimensional super-gravity theory as an anomalous gauge theory. There, the anomaly-cancelling super-Liouville fields are succesfully introduced to identify the original second-class constrained system with a gauge-fixed version of a first-class system. These results have been reported at "The International Symposium on BRS symmetry on the Occasion of Its 20th Anniversary" which was held at the Research Institute for Matimatical Sciences, Kyoto University for Septmber 18-22,1995.Our method has been applied also to a topological BF theory with an antisymmetric tensor field.We investigated if the system can contain gauge anomaly by using the general cohomological analysis based on the BFV formalism. The main results that the system have no BRS anonalies was reported at The Autumn Meeting of the Japan Physical Sociaty held at Chuoh University, September 1995.