AI 中文总结
本文研究Mielke–Baekler几何中的有质量与无质量自旋粒子，利用余伴随轨道和非线性实现构造其世界线作用量，分析远平行分支的联络性质、自旋相关的动力学区域及不同质量粒子的对称性。
AI 中文摘要
Mielke–Baekler几何是三维约化齐次时空，配有与洛伦兹度量相容的不变联络。这类时空推广了闵可夫斯基和（反）德西特时空，其不变度量联络可具有挠率，这是三维的特有性质。利用余伴随轨道和非线性实现技术，我们构造了在这类时空中运动的有质量和无质量自旋粒子的世界线作用量。我们特别关注所谓的远平行分支，其中不变联络的曲率为零。除平凡的闵可夫斯基情形外，该分支仅选出反德西特时空作为这些洛伦兹流形中唯一容许不变Weitzenböck联络（即带挠率的平坦联络）的流形。引入描述自旋的Wess–Zumino项的主要结果是出现动力学区域（记为“正则”和“临界”），具有不同数量的物理自由度。特别地，在有质量情形中，我们讨论用Weitzenböck联络或Levi-Civita联络表述的动力学，以及临界区域中Papapetrou型强迫项的出现。对于无质量粒子，我们研究作用量的诺特定理对称性，对于无自旋情形，其包含共形变换；对于非零自旋，正则区域中仅基灵子集作为真正的诺特变换保留，而临界区域中任何共形基灵贡献都可通过规范变换置零。
英文摘要
The Mielke--Baekler geometries are three-dimensional reductive homogeneous spacetimes together with a choice of invariant connection which is compatible with a lorentzian metric. The spacetimes generalise Minkowski and (anti)de~Sitter spacetimes in that the invariant metric connection can have torsion, a peculiarity of three dimensions. Using coadjoint orbits and the techniques of nonlinear realisations, we construct worldline actions for massive and massless spinning particles moving in these spacetimes. We pay particular attention to the so-called teleparallel branch, in which the curvature of the invariant connection vanishes. Apart from the trivial Minkowski case, this singles out anti-de~Sitter spacetime, as the only of these lorentzian manifolds admitting an invariant Weitzenböck connection; that is, a flat connection with torsion. The introduction of a Wess--Zumino term describing spin has, as a main consequence, the appearance of dynamical sectors (denoted ``regular'' and ``critical''), with a different number of physical degrees of freedom. In particular, in the massive case, we discuss the formulation of the dynamics in terms of either the Weitzenböck or the Levi-Civita connection, and the emergence of a Papapetrou-type forcing term in the critical sector. For the massless particle we study the Noether symmetries of the action, which, for the spinless case, include the conformal transformations. For nonzero spin, only the Killing subset survives as genuine Noether transformations in the regular sector, while in the critical sector any conformal Killing contribution can be set to zero by a gauge transformation.
Comments55 pages, no figures. Added reference [40]
