无穷维Hilbert空间的模函子
Modular functors with infinite dimensional Hilbert spaces
摘要：
本文在一般无限维Hilbert空间中引入了广义模函子的概念，并证明了具有共形维数的广义模函子唯一地确定波函数为其平坦截面.此外，我们还研究了一个由Liouville共形场论导出的广义模函子的例子。在这个例子中，波函数被看作是胶合共形块，它们与量子泰希米勒理论中的本征函数相一致。
英文摘要：
We introduce a notion of generalized modular functors with Hilbert spaces of infinite dimension in general, and show that a generalized modular functor with data of conformal dimensions determines uniquely wave functions as its flat sections. Furthermore, we study an example of generalized modular functors derived from the Liouville conformal field theory. In this example, wave functions are seen to be gluing conformal blocks which are identified with eigenfunctions in the quantum Teichmüller theory.
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