AI 中文总结
本文发展R-仿统计的理论基础与扩展，构建三类局域可观测量及广义隐藏对称性，为区分R-仿粒子与费米子、玻色子及观测其性质奠定基础，推动相关量子信息等应用研究。
AI 中文摘要
仿统计是超越费米子和玻色子的一种奇特交换统计类型，仿粒子在交换对称群的高维表示中变换，类似于非阿贝尔任意子，但可在任意维度中一致定义。尽管仿粒子早已被提出，但长期以来人们普遍认为它们在物理上等价于费米子或玻色子。不过，最近一篇论文提出了一种不同的理论，称为R-仿统计，并证明非平凡的R-仿粒子可以作为凝聚态系统中的准粒子出现，且与费米子和玻色子明显可区分。本文发展了R-仿统计的理论基础及若干扩展，特别强调其可观测后果。本文的核心是扩展之前引入的基本族的局域可观测量的一般理论：首先，定义可区分粒子类型的局域可观测量；其次，构建在特殊点缺陷处的局域可观测量，这些可观测量探测R-仿粒子的内部指标，对观测R-仿统计及其在量子信息中的拟议应用至关重要；第三，引入可产生或湮灭粒子-反粒子对的局域可观测量，这对构建R-仿粒子的相对论量子场理论很重要。我们还引入了广义隐藏对称性，其作用于R-仿粒子的内部指标同时保持局域可观测量代数，为证明局域不可区分性及连接R-仿统计的范畴描述提供基础。这项工作为理解R-仿粒子的基本物理性质奠定了坚实的理论基础，并为在自然界中发现它们铺平了道路。
英文摘要
Parastatistics is an exotic type of exchange statistics beyond fermions and bosons. Paraparticles transform in higher dimensional representations of the exchange symmetry group, analogous to non-Abelian anyons, yet consistently defined in any dimension. Although paraparticles have long been proposed, they were widely believed to be physically equivalent to fermions or bosons. Nevertheless, a recent paper proposed a different theory, called $R$-parastatistics, and demonstrated that nontrivial $R$-paraparticles can emerge as quasiparticles in condensed matter systems, and are observably distinct from both fermions and bosons. This paper develops the theoretical foundation and several extensions of $R$-parastatistics, with particular emphasis on its observable consequences. Central to this paper is a general theory of local observables extending the basic family introduced before. First, we define local observables that distinguish particle types. Second, we formulate local observables at special point defects that probe the internal indices of $R$-paraparticles, crucial for observing $R$-parastatistics and for the proposed applications in quantum information. Third, we introduce local observables that create or annihilate particle-antiparticle pairs, important for building a relativistic quantum field theory for $R$-paraparticles. We further introduce generalized hidden symmetries that act on internal indices of $R$-paraparticles while preserving the local observable algebra, providing a basis for proving local indistinguishability and for connecting to a categorical description of $R$-paraparticles. This work sets a solid theoretical foundation for understanding the fundamental physical properties of $R$-paraparticles and pave the way for finding them in nature.
Comments56 pages, 7 captioned figures
