标题： 可逆准粒子和扩展激发的统计定义，使用多体希尔伯特空间上的算子 显示英文标题

标题： Definition for statistics of invertible quasi-particles and extended excitations using operators on many-body Hilbert space

摘要： 在本文中，我们开发了一个数学框架，该框架基于多体希尔伯特空间中的字符串算符，将阿贝尔任意子的统计定义进行推广，以适用于任意维数的可逆拓扑激发在任意流形上的情况。 该理论是严格且系统的，并为理解和证明统计性质提供了通用框架。 此外，我们提出了几个可能具有数学兴趣的猜想。 我们还提出了一种用于计算统计的计算机程序，其结果与其他物理理论的预测一致。 显示英文摘要

摘要： In this paper, we develop a mathematical framework that generalizes the definition of statistics for Abelian anyons, based on string operators in many-body Hilbert space, to arbitrary dimensions of invertible topological excitations on arbitrary manifolds. This theory is rigorous, systematic, and provides a general framework for understanding and proving the properties of statistics. Additionally, we propose several conjectures that may hold mathematical interest. We also present a computer program for calculating statistics, which has yielded results consistent with predictions from other physical theories.