论文标题
排列阶段和外邦统计
Permutation Phase and Gentile Statistics
论文作者
论文摘要
本文提出了一种构建与费米和Bose统计之间具有中间交换阶段的相同粒子的单体多体波形的新方法。可以证明，交换阶段不是代表性字符，而是排列组的\ textIt {word metric}，超出了二维组的辫子群体。通过从单粒子状态的直接乘积构造这种类型的波函数，可以表明有限\ textit {容量q} - 自然会出现每个量子状态的最大允许粒子占用。给出了置换阶段和容量之间的关系，在交换阶段和职业数字的意义上，费米子和玻色子之间进行了插值。这为\ textit {Gentile Statistics}和新方向提供了量子力学基础，以探索中间统计和任何人。
This paper presents a new way to construct single-valued many-body wavefunctions of identical particles with intermediate exchange phases between Fermi and Bose statistics. It is demonstrated that the exchange phase is not a representation character but the \textit{word metric} of the permutation group, beyond the anyon phase from the braiding group in two dimensions. By constructing this type of wavefunction from the direct product of single-particle states, it is shown that a finite \textit{capacity q} -- the maximally allowed particle occupation of each quantum state, naturally arises. The relation between the permutation phase and capacity is given, interpolating between fermions and bosons in the sense of both exchange phase and occupation number. This offers a quantum mechanics foundation for \textit{Gentile statistics} and new directions to explore intermediate statistics and anyons.
