Particles of generalized statistics, quantum logic and categories

Particles, Generalized Statistics and Categories

Interacting systems of particles with generalized statistics are considered on both classical and quantum level. It is shown that all possible quantum states and corresponding processes can be represented in terms of certain specific categories. The corresponding Fock space representation is discussed. The problem of existence of well--defined scalar product is considered. It is shown that commutation relations corresponding to a system with generalized statistics can be constructed from relations corresponding to Bolzman statistics.

拓扑量子场论的自旋-统计定理

The spin-statistics theorem for topological quantum field theories

本文在Atiyah框架下通过引入费米子dagger紧致范畴，证明了拓扑量子场论的自旋-统计定理，并统一了自旋结构、超向量空间与幺正性。

Dimension as a quantum statistic and the classification of metaplectic categories

We discuss several useful interpretations of the categorical dimension of objects in a braided fusion category, as well as some conjectures demonstrating the value of quantum dimension as a quantum statistic for detecting certain behaviors of anyons in topological phases of matter. From this discussion we find that objects in braided fusion categories with integral squared dimension have distinctive properties. A large and interesting class of non-integral modular categories such that every simple object has integral squared-dimensions are the metaplectic categories that have the same fusion r…