Research in Gravitation and Quantum Field Theory

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Research will focus on three distinct, but interrelated areas of research: quantum gravity and its generalizations, classical gravitation theories and quantum field theory. The main problems to be considered include the following: Conformal anomalies in general space-time dimensions and their applications, following on results obtained very recently. This subject cuts across all three main topics, with consequences for both classical gravity and quantum field theory, for example in extending two-dimensional field theoretical theorems to four dimensions. The properties of quantum gravity in the ultra-high energy domain will be studied to establish whether this regime can be understood independent of the complications of the full theory, just as can the low energy sector. In particular, possible relations to topological theories will be investigated; again preliminary progress is encouraging and will provide the starting point. The role of the self-energy problem for ultra-rapid particles must be considered both in the above context and as an intrinsically important aspect of gravity theories; is there an improvement over the difficulties encountered by massive sources? The definition of energy, central to understanding the solutions of two-dimensional gravity should be uniquely settled by systematic application of the well-understood methodology originally developed for general relativity. While the properties of two-and three- dimensional gravity have provided much insight and have been a central aspect of recent research, the qualitatively different domain of high dimensions has not yet received attention. Any simplifications or unusual features at high D would also yield a deeper understanding, and this sector of gravity will also be probed. The role of scalar fields in gravitation has been pervasive, most recently under the impetus of string theory, as well as in connection with conformal invariance. Nevertheless, there is still no systematic unde rstanding of the possible physical effects of scalars. At their most optimistic, these might include an alternate approach to the Higgs problem at a fundamental level.