Quantum Field Theory, Noncommutative Geometry and Supergeometry

这个项目的主要目标是应用现代数学的方法来解决理论物理中出现的问题。 许多问题都与M理论有关。 这个理论可以被认为是弦理论的一个扩展。 M理论描述了自然界中存在的所有相互作用。 M理论可以表述为一个矩阵模型，称为M（atrix）理论。 在这种方法中很清楚，物理空间的几何在某种意义上是非交换的，因此应用非交换几何的方法是很自然的。 这个想法被用于制定一些项目，以及在我们最近的工作有关的环形紧化的M（矩阵）理论。 大部分的其他问题都涉及到超几何的应用，量子场论的各种问题，包括量子化的规范理论和拓扑量子场论的一般问题。这个多学科的研究是由数学科学部，物理部，和数学和物理科学主任的多学科活动办公室联合资助。

AbstractSchwarzThe main goal of this project is to apply methods of modern mathematics to problems arising in theoretical physics. Many of problems are related to M-theory. This theory can be considered as an extension of string theory. It is believed that M-theory describes all interactions existing in nature. It was conjectured recently that M-theory can be formulated as a matrix model, called M(atrix) theory. It is clear in this approach that the geometry of physical space is non-commutative in some sense, and so it is natural to apply methods of non-commutative geometry. This idea was used in the formulation of some projects as well as in our recent work concerning toroidal compactifications of M(atrix) theory. Most of the other problems are related to applications of super-geometry to various problems of quantum field theory, including general problems of quantization of gauge theories and topological quantum field theory.This multidisciplinary research is jointly funded by the Division of Mathematical Sciences, the Division of Physics, and the Office of Multidisciplinary Activity of the Director of Mathematical and Physical Sciences.