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：在最近取得的结果的基础上，一般时空维度中的共形反常及其应用。这一主题跨越了所有三个主要主题，对经典引力理论和量子场论都有影响，例如将二维场理论定理扩展到四维。我们将研究超高能领域中量子引力的性质，以确定是否可以像理解低能领域那样，独立于完整理论的复杂性来理解这一体系。特别是，将调查可能与拓扑学理论的关系；同样，初步进展令人鼓舞，并将提供起点。超快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内在重要方面来考虑；对于大质量源所遇到的困难，是否有改进？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广为人知的方法来唯一地解决。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的情况下，任何简化或不寻常的特征也会产生更深层次的理解，这一部分的重力也将被探讨。标量场在引力中的作用一直很普遍，最近在弦理论的推动下，在共形不变性方面也是如此。然而，仍然没有系统地了解标量可能产生的物理效应。在他们最乐观的情况下，这些可能包括从根本上解决希格斯问题的另一种方法。

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.