Quantum field theory with gravity and anomalies

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The main subjects of this research project, namely, the problems related to anomalies, topology and Riemann surfaces received much attention recently.As for the specific results of the present research project, K. Fujikawa studied the detailed behavior of non-critical strings. By regarding the non- critical string theory as a 2-dimensional quantum gravity with anomalies, it was shown that the BRS symmetry is quite naturally defined for a free non- critical string. The string interactions are, however, rather involved due to the topological constraints related to the Riemann-Roch theorem (or ghost number anomaly).T. Kimura formulated a general quantum treatment of constrained systems, which are closely related to the quantum gravity. The applications of this formulation are left for the future.A. Hosoya studied the various problems related to the topology changes in quantum gravity. To be specific, he analyzed the vanishing mechanism of the cosmological constant due to baby universes in the path integral formalism. At the same time, he discovered a new instanton-like gravitational solution. As for 3-dimensional quantum gravity, he gave a nice canonical formulation by using the Teichmuller parameters as dynamical variables.S. Uehara continued the study of super-strings and super-particle. In particular, he succeeded in the general formulation to deal with the deformations of super-Riemann surfaces. This analysis, which is mathematically interesting, is hoped to provide a new insight into the dynamics of super- strings.