量子统计与时空手术
Quantum Statistics and Spacetime Surgery
摘要：
我们应用时空流形上的几何拓扑手术理论研究了2+1和3+1维时空中量子统计数据的约束。首先，我们介绍了融合数据的世界线和世界表运营商能够创建任意子激发的粒子和字符串，定义良好的带隙状态的物质与内在的拓扑秩序。其次，我们介绍了封闭时空3-流形和4-流形中粒子和弦的编织统计数据，如粒子弦Aharonov-Bohm的几何Berry矩阵和多圈绝热编织过程的子流形连接编码。第三，我们推导出新的量子手术约束类似于Verlinde公式，通过时空手术将融合和编织统计数据关联起来，这对于定义拓扑序理论至关重要，并且可能与自举边界物理学（如无隙模式，共形场论或量子异常）相关。
英文摘要：
We apply the geometric-topology surgery theory on spacetime manifolds to study the constraints of quantum statistics data in 2+1 and 3+1 spacetime dimensions. First, we introduce the fusion data for worldline and worldsheet operators capable creating anyon excitations of particles and strings, well-defined in gapped states of matter with intrinsic topological orders. Second, we introduce the braiding statistics data of particles and strings, such as the geometric Berry matrices for particle-string Aharonov-Bohm and multi-loop adiabatic braiding process, encoded by submanifold linkings, in the closed spacetime 3-manifolds and 4-manifolds. Third, we derive new quantum surgery constraints analogous to Verlinde formula associating fusion and braiding statistics data via spacetime surgery, essential for defining the theory of topological orders, and potentially correlated to bootstrap boundary physics such as gapless modes, conformal field theories or quantum anomalies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
