非阿贝尔几何与圆柱狄拉克二重态的全局不等价对称约化
Global structure and holonomy of conserved resolutions in the cylindrical Dirac doublet
- University of Science and Technology Beijing（北京科技大学）
- Tsinghua University（清华大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究圆柱狄拉克二重态的对称约化，发现其三种对称选择的秩1约化局部等价但全局结构不同，推导了对应方位角威尔逊环谱，揭示了非阿贝尔几何特性。
AI中文摘要：
不同的精确圆柱狄拉克构造在同一二维正能量扇区内局部相关，表明它们可能仅是基的替代选择。我们证明这种等价性在全局层面会失效。将圆柱狄拉克二重态视为动量空间上的秩2丛，我们识别出横向螺旋度、质量修饰横向积分以及螺旋度三种由对称选择的秩1约化，其归一化限制通过泡利代数组织内部二重态。正能量狄拉克SU(2)联络在横向螺旋度基下于固定方位子午线上精确阿贝尔化，而对于非零质量，其完整三维曲率仍为真正的非阿贝尔。我们以闭式形式推导对应的方位角威尔逊环谱。三种约化呈现截然不同的全局结构：横向螺旋度分裂终止于动量轴，质量修饰分裂平滑延伸且在m>0时为陈平凡，而螺旋度定义具有相反单位陈数的线丛。因此单个狄拉克二重态可具有局部等价但全局不等价的对称分解。
英文摘要：
Cylindrical Dirac modes underlie constructions in rotating QCD matter, boost-invariant Dirac-field quantization in heavy-ion physics, and high-energy twisted-particle scattering. The corresponding complete spinor frames can be regarded as alternative bases, but their equivalence does not determine the global behavior of eigenlines selected by conserved observables. Within the positive-energy doublet of the free massive Dirac Hamiltonian, we compare three conserved resolutions: $K$, which couples spin to transverse momentum; $K_m$, a mass-dependent operator derived from the transverse Dirac Hamiltonian; and helicity. On the common regular domain away from the momentum axis, explicit smooth, single-valued $SU(2)$ transformations relate all three splittings. Although globally $SU(2)$-equivalent on this common domain, they exhibit three distinct global extension behaviors. The $K$ projectors have azimuth-dependent polar limits and do not extend continuously to the axis. For nonzero mass, the $K_m$ projectors extend smoothly over the enclosed momentum ball and define Chern-trivial eigenlines. The helicity projectors are smooth on every nonzero momentum sphere, but their eigenlines carry opposite unit Chern numbers and cannot extend through the enclosed origin. The parent positive-energy Dirac connection Abelianizes exactly in the $K$ eigenlines on fixed-azimuth meridians, whereas its full three-dimensional curvature has noncommuting components. We obtain the azimuthal Wilson loop in closed form and derive the exact conversion probability between the two $K$ branches under purely geometric positive-energy transport.
