Research in Gravitation and Quantum Field Theory

研究将集中在三个不同但相互关联的研究领域：量子引力及其推广，经典引力理论和量子场论。 要考虑的主要问题包括：在一般时空维度的共形异常及其应用，最近获得的结果。 这门学科贯穿了所有三个主要主题，对经典引力和量子场论都有影响，例如将二维场论定理扩展到四维。 我们将研究超高能域中量子引力的性质，以确定这个区域是否可以独立于完整理论的复杂性来理解，就像低能区一样。 特别是，可能的关系拓扑理论将进行调查;再次初步进展是令人鼓舞的，并将提供起点。 超高速粒子的自能问题的作用必须在上述背景下考虑，并作为引力理论的一个本质上重要的方面;是否有一个改进的困难所遇到的大规模来源？ 能量的定义是理解二维引力解的核心，应该通过系统地应用最初为广义相对论开发的已被充分理解的方法来解决。 虽然二维和三维引力的性质提供了许多见解，并已成为最近研究的一个中心方面，但高维的性质不同的领域尚未受到关注。 在高D处的任何简化或不寻常的特征也将产生更深的理解，并且也将探测这一引力区域。 标量场在引力中的作用一直很普遍，最近是在弦理论的推动下，以及与共形不变性有关。 然而，对于标量可能的物理效应还没有系统的认识。 在他们最乐观的情况下，这些可能包括在根本层面上解决希格斯问题的替代方法。

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.