We use radial quantization to compute Chern-Simons partition functions on handlebodies of arbitrary genus. The partition function is given by a particular transition amplitude between two states which are defined on the Riemann surfaces that define the (singular) foliation of the handlebody. The final state is a coherent state while on the initial state the holonomy operator has zero eigenvalue. The latter choice encodes the constraint that the gauge fields must be regular everywhere inside the handlebody. By requiring that the only singularities of the gauge field inside the handlebody must be compatible with Wilson loop insertions, we find that the Wilson loop shifts the holonomy of the initial state. Together with an appropriate choice of normalization, this procedure selects a unique state in the Hilbert space obtained from a Kähler quantization of the theory on the constant-radius Riemann surfaces. Radial quantization allows us to find the partition functions of Abelian Chern-Simons theories for handlebodies of arbitrary genus. For non-Abelian compact gauge groups, we show that our method reproduces the known partition function at genus one.

我们使用径向量化来计算任意属的手柄上的 Chern-Simons 分区函数。分配函数由定义在黎曼曲面上的两个状态之间的特定过渡幅度给出，该黎曼曲面定义了手柄主体的（单一）叶理。最终状态是相干状态，而在初始状态，完整算子的特征值为零。后一种选择对规范场必须在手柄内的任何地方都是规则的约束进行编码。通过要求手柄内规范场的唯一奇点必须与威尔逊环插入兼容，我们发现威尔逊环改变了初始状态的完整度。再加上适当的归一化选择，此过程在 Hilbert 空间中选择一个独特的状态，该状态是从恒定半径黎曼曲面上的理论的 Kähler 量化获得的。径向量化允许我们找到任意属的把手的阿贝尔陈 - 西蒙斯理论的配分函数。对于非阿贝尔紧致规范群，我们表明我们的方法在属 1 处再现了已知的配分函数。