The Mathematics of Conformal Field Theory

共形场论是量子场论，其可测量量在共形坐标变化下是不变的，也就是说，坐标变换保留角度，但不一定保留长度。事实证明，在二维时空中存在无限多个独立的（局部）共形变换。这意味着二维共形场论有无限多的约束来自于共形对称。这些无限的约束使得精确地解决（一些）共形场理论成为可能，并允许人们避免使用近似或数学上不明确的概念，如路径积分。共形不变性赋予了共形场理论丰富的数学结构。这种数学结构使共形场理论成为数学研究的一个活跃话题，探索它将构成本项目的核心

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