The Mathematics of Conformal Field Theory

共形场论（英语：Conformal field theory）是一种量子场论，其可测量的量在坐标的共形变化下是不变的，即坐标变换保持角度，但不一定是长度。事实证明，在2个时空维度中，有无限多个独立的（局部）共形变换。这意味着二维共形场论有无穷多个来自共形对称的约束。这些无限的约束使得（某些）共形场论的精确解成为可能，并使人们避免使用近似或数学上不好定义的概念，如路径积分。共形不变性赋予共形场论丰富的数学结构。这种数学结构是什么使共形场论的数学研究的一个活跃的话题，探索它将形成这个项目的核心

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