Application of methods of arithmetic geometry and homological algebra to quantum field theory and string theory

[摘要]获奖：dms -0805989首席研究员：Albert schwarz这些项目中的第一个是关于p-adicmethods在拓扑弦上的应用。这些项目的目标是用等差几何上进数来表示物理量，并使用这些表达式来证明完整性定理。另一组研究涉及量子场论的超对称变形。这是与M. Movshev的联合工作，并应用了l -∞和a -∞代数理论。另一个项目致力于分析弦论和量子场论之间的关系。首席研究员认为，量子场论可以表述为这样，时间和空间似乎不是主要概念，并计划证明弦理论可以被视为这种意义上的量子场论。这些研究项目是基于现代数学方法在物理中的应用，特别是利用算术几何和同调代数来提高我们对量子场论和弦理论的理解。复杂的数学最初发展为其他目的，如研究丢番图方程在数论似乎直接承担在理论物理的挑战问题。

AbstractAward: DMS-0805989Principal Investigator: Albert SchwarzThe first of these projects concerns applications of p-adicmethods to topological strings. The goal of these projects is toexpress physical quantities in terms of arithmetic geometry overp-adic numbers and to use these expressions to prove integralitytheorems. Another set of investigations deals withsupersymmetric deformations of quantum field theories. This isjoint work with M. Movshev and applies the theory of L-infinityand A-infinity algebras. Another project is devoted to theanalysis of the relation between string theory and quantum fieldtheory. The principal investigator has argued that quantum fieldtheory can be formulated such that time and space do not appearas primary notions, and is planning to show that string theorycan be regarded as a quantum field theory in this sense.These research projects are based on the application of methodsof modern mathematics to physics, particularly making use ofarithmetic geometry and homological algebra to improve ourunderstanding of quantum field theory and string theory.Sophisticated mathematics originally developed for other purposessuch as the study of Diophantine equations in number theory seemsto bear directly on challenging issues in theoretical physics.