发表机构
International School for Advanced Studies (SISSA); National Institute for Nuclear Physics (INFN), Sezione di Trieste; Institute for Fundamental Physics of the Universe (IFPU); National Centre for Nuclear Research（高级研究国际学院; 意大利国家核物理研究所的里雅斯特分部; 宇宙基础物理研究所; 国家核研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究三维圆形角扩展对称群的表示论，构造表示族并分析酉性、不可约性及中心扩张，为量子引力中角自由度的系统描述奠定基础。
AI 中文摘要
我们研究了与圆形角相关联的三维扩展角对称群的表示论。利用诱导表示技术，我们构造了无限维角对称群的表示族，并分析了它们的酉性和不可约性。我们还确定了该对称群的最大中心扩张，并构造了相应的射影表示。该分析的动机源于角对称性在量子引力中所扮演的角色，其中边界自由度——受角变换作用——预计编码了时空量子结构的某些方面。在三维中，出现的表示论结构与已经作为引力研究核心的对称群和量子理论密切相关。这项工作为三维量子引力角自由度的系统描述迈出了第一步。
英文摘要
We study the representation theory of the three-dimensional extended corner symmetry group associated with a circular corner. Using induced representation techniques, we construct families of representations of the infinite-dimensional corner symmetry group and analyze their unitarity and irreducibility. We also determine the maximal central extension of the symmetry group and construct the corresponding projective representations. The analysis is motivated by the role that corner symmetries play in quantum gravity, where boundary degrees of freedom --- acted upon by the corner transformations --- are expected to encode aspects of the quantum structure of spacetime. In three dimensions, the representation-theoretic structures that emerge are closely related to symmetry groups and quantum theories that already appeared as central to the study of gravity. This work provides a first step toward a systematic description of quantum gravitational corner degrees of freedom in three dimensions.
Comments50 pages, 1 figure
