Research in Gravitation and Quantum Field Theory

研究将集中在三个不同的，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：一般时空维度的共形异常及其应用，以下是最近得到的结果。这个主题跨越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。量子引力在超高能量域中的性质将被研究，以确定是否可以独立于完整理论的复杂性来理解这一制度，就像低能量领域一样。特别是，可能的关系拓扑理论将被调查；同样，初步进展令人鼓舞，并将提供一个起点。超高速粒子的自能问题的作用必须在上述背景下加以考虑，并作为引力理论的一个本质上重要的方面加以考虑；大量资源所遇到的困难是否有所改善？能量的定义是理解二维重力解的核心，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唯一地解决。虽然二维和三维重力的性质已经提供了许多见解，并已成为最近研究的一个中心方面，但在质量上不同的高维领域尚未得到重视。在高D的任何简化或不寻常的特征也将产生更深入的理解，这部分的重力也将被探索。标量场在引力中的作用已经无处不在，最近在弦理论的推动下，以及与共形不变性有关。然而，对于标量可能产生的物理效应仍然没有系统的认识。在他们最乐观的情况下，这些可能包括在基本层面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.