arXiv 1706.013752017-06hep-thgr-qc

三维重力场耦合粒子的有效Chern-Simons作用量

Effective Chern-Simons actions of particles coupled to 3D gravity

Tomasz Trześniewski

备注：: 15 pages, v2 several formulae, remarks and references added, v3 summary extended and references added
发表信息：: Nucl. Phys. B 928, 448 (2018)
DOI：: 10.1016/j.nuclphysb.2018.01.023

摘要：

三维引力场中的点粒子是拓扑亏损的，而引力场可以表示为时空的适当定域等距群的Chern-Simons理论。在庞加莱群的情况下，积分出引力自由度，就有可能得到粒子动力学的有效作用量。我们回顾了单粒子和多粒子的已知结果，并试图将这种方法推广到（反）德西特群，使用等距群的因子分解为洛伦兹群和AN（2）群的双重乘积。另一方面，对于de Sitter群，也可以对AN（2）和平移群的半直积进行收缩。相应的有效作用量奇妙地描述了一个具有AN（2）动量空间的卡罗粒子。我们推导出这种收缩在一个更严格的方式，并进一步探讨其性质，包括推广到多粒子的情况下。

英文摘要：

Point particles in 3D gravity are known to behave as topological defects, while gravitational field can be expressed as the Chern-Simons theory of the appropriate local isometry group of spacetime. In the case of the Poincaré group, integrating out the gravitational degrees of freedom it is possible to obtain the effective action for particle dynamics. We review the known results, both for single and multiple particles, and attempt to extend this approach to the (anti-)de Sitter group, using the factorizations of isometry groups into the double product of the Lorentz group and AN(2) group. On the other hand, for the de Sitter group one can also perform a contraction to the semidirect product of AN(2) and the translation group. The corresponding effective action curiously describes a Carrollian particle with the AN(2) momentum space. We derive this contraction in a more rigorous manner and further explore its properties, including a generalization to the multiparticle case.

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英文摘要：

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