The Mathematics of Conformal Field Theory

共形场论的数学

• 批准号: 2108968
• 金额: --
• 依托单位: CARDIFF UNIVERSITY
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2108968
• 关键词: Mathematics; Conformal; Field; Theory

Conformal field theories are quantum field theories whose measurable quantities are invariant under conformal changes of coordinates, that is, coordinate transformations which preserve angles, but not necessarily lengths. It turns out that in 2 space-time dimensions there are infinitely many independent (local) conformal transformations. This means that 2 dimensional conformal field theories have infinitely many constraints coming from conformal symmetry. These infinite constraints are what make it possible to solve (some) conformal field theories exactly and allow one to avoid using approximations or mathematically ill defined notions such as path integrals.Conformal invariance endows conformal field theories with a rich mathematical structure. This mathematical structure is what makes conformal field theory an active topic of mathematical research and exploring it will form the core of this project

共形场论是一种量子场论，其可测量量在坐标共形变化下保持不变，即保持角度但不一定保持长度的坐标变换。事实证明，在 2 个时空维度中存在无限多个独立（局部）共形变换。这意味着二维共形场论有无数来自共形对称性的约束。这些无限约束使得精确求解（某些）共形场论成为可能，并允许人们避免使用近似或数学上定义错误的概念（例如路径积分）。共形不变性赋予共形场论丰富的数学结构。这种数学结构使共形场论成为数学研究的活跃主题，对其进行探索将构成该项目的核心