AI 中文总结
研究多体多极子分类问题，利用与旋转兼容的规范对称性，通过两个附加标签实现十六重分类，可组织多体多极子空间中相关选择规则。
AI 中文摘要
传统的多极子框架为单电子自由度提供了一种基于对称性的标准语言，但无法区分多体算符空间中物理上不同的扇区。我们表明，与旋转兼容的规范对称性通过与粒子数规范变换\(G{\pi}/2\)和粒子-空穴变换\(CA\)相关的两个附加标签提供了这种结构。这些标签分离了具有不同体数和粒子数变化的算符，从而导致十六重分类，该分类组织了多体多极子空间中非零期望值选择规则、诱导多极子和对称允许耦合的选择规则。
英文摘要
The conventional multipole framework provides a standard symmetry-based language for one-body electronic degrees of freedom, but fails to distinguish physically distinct sectors in many-body operator space. We show that canonical symmetries compatible with rotations provide this structure through two additional 2 labels associated with the particle-number gauge transformation Gπ/2 and the particle-hole transformation CA. These labels separate operators with different body numbers and particle-number changes, leading to a sixteenfold classification that organizes selection rules for nonzero expectation values, induced multipoles, and symmetry-allowed couplings in many-body multipole space.
