标题： 可逆拓扑激发的统计：一种使用算子和多体希尔伯特空间的框架 显示英文标题

标题： Statistics of invertible topological excitations: a framework using operators and many-body Hilbert spaces

摘要： 在本文中，我们开发了一个数学框架，该框架基于字符串算子和多体希尔伯特空间，推广了任意子统计的概念，以适用于任何维度的可逆拓扑激发。 该框架仅建立在量子力学的几个基本事实之上，同时为与拓扑序和场论无关的统计提供了严格且系统的理论。 此外，我们提出了几个可能具有数学兴趣的猜想。 我们还提供了一个用于计算统计的计算机程序，其结果与传统物理理论一致。 显示英文摘要

摘要： In this paper, we develop a mathematical framework that generalizes the concept of anyon statistics, based on string operators and many-body Hilbert space, to invertible topological excitations of any dimensions. This framework is only build on several fundamental facts in quantum mechanics, while providing a rigorous and systematic theory for statistics independent to topological order and field theory. Additionally, we propose several conjectures that may hold mathematical interest. We also present a computer program for computing statistics, which has yielded results consistent with traditional physical theories.