标题： 粒子，广义统计和范畴 显示英文标题

标题： Particles, Generalized Statistics and Categories

摘要： 考虑在经典和量子层面上具有广义统计的粒子相互作用系统。 已经证明，所有可能的量子态和相应的过程都可以用某些特定范畴来表示。 讨论了相应的福克空间表示。 考虑了存在定义良好的标量积的问题。 已经证明，对应于广义统计系统的对易关系可以从对应于玻尔兹曼统计的关系中构造出来。 显示英文摘要

摘要： 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.