Holomorphic and quantum aspects of generalized Kahler geometry

广义卡勒几何的全纯和量子方面

• 批准号: 355576-2013
• 负责人: Gualtieri, Marco
• 金额: $ 2.77万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635355
• 关键词: Holomorphic; quantum; aspects; generalized; Kahler

Mathematical models which are used to describe the behaviour of physical systems are often based on geometrical structures on complex curved spaces of potentially large dimension. This is true when studying mechanics, the physics of elementary particles, the behaviour of superconductors, and in many other cases. The discovery of increasingly complicated physical systems in quantum field theory has led to the development of new and interesting types of geometric structure, which differ drastically from traditional geometric forms, and so are not well understood.In key areas of theoretical physics such as renormalization and quantum gravity, progress is slowed when physicists are not able to access appropriate mathematical tools for modelling the physical systems of interest. In some cases, such mathematical tools have simply not yet been invented.The goal of the proposed research is to develop a mathematical understanding of a certain class of geometric structures called generalized Kahler structures, to discover the underlying fundamental laws which govern similar structures which arise in quantum field theory, and finally to use the powerful tools of algebraic and differential geometry to leap forward by inventing new geometric structures which help pave the way toward better models in the future.

用于描述物理系统行为的数学模型通常基于潜在大维度的复杂弯曲空间上的几何结构。在研究力学、基本粒子物理学、超导体的行为以及许多其他情况时，这都是正确的。量子场论中越来越复杂的物理系统的发现导致了新的有趣的几何结构类型的发展，这些几何结构与传统的几何形式有很大的不同，因此还没有得到很好的理解。在理论物理的关键领域，如重整化和量子引力，当物理学家不能获得适当的数学工具来模拟感兴趣的物理系统时，进展就会减慢。在某些情况下，这样的数学工具还没有被发明出来。拟议研究的目标是发展对一类称为广义Kahler结构的几何结构的数学理解，发现量子场论中出现的支配类似结构的基本定律，最后，利用代数和微分几何的强大工具，通过发明新的几何结构，为未来更好的模型铺平道路，实现飞跃。