Mathematical Sciences: Mathematical Problems of Quantum Field Theory

小行星9500704施瓦茨 该提案包括几个项目，致力于量子场论的数学问题。 特别是，我们正计划使用超几何的技术来证明新的定理， 半经典近似的精确性。量子场论的方法将被用来构造不变量 一些几何结构。几乎所有的项目都与弦理论有关，弦理论现在被认为有机会 描述自然界中存在的所有相互作用。我们将尝试建构假设的“万有弦理论”，并对空间的维度达成更深的了解 在弦理论中，使用公理化量子场论的方法。 量子场论是一门与数学和物理学的中心研究领域重叠的学科。 在物理学中，它是 试图理解所有物质的基本粒子 形成了 在数学中，它是一种技术，具有广泛的 在几何、分析和概率等领域的应用。 的 这项研究背后的根本目标是朝着这个目标取得进展， 揭示统一自然力的基本理论的重要性 ***

9500704 Schwarz The proposal consists of several projects, devoted to mathematical problems of quantum field theory. In particular, we are planning to use the technique of supergeometry to prove new theorems giving conditions of exactness of semiclassical approximation. The methods of quantum field theory will be used to construct invariants of some geometric structures. Almost all projects are related to string theory, which is now considered as having a chance to describe all interactions existing in Nature. We will try to construct the hypothetical "universal string theory" and reach a deeper understanding of the dimensionality of the space in string theory, using methods of axiomatic quantum field theory. Quantum field theory is a subject which overlaps central areas of research in both mathematics and physics. In physics it is at the heart of the attempt to understand the fundamental particles from which all matter is formed. In mathematics it is a body of techniques which have wide applications in areas such as geometry, analysis and probability. The underlying goal behind this research is to make progress towards the aim of uncovering the fundamental theory which unifies the forces of nature. ***