BMS$_3$ 模来自共伴随轨道上的路径积分
BMS$_3$ modules from path integrals on the coadjoint orbits
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中文总结 AI 辅助
本文通过一圈路径积分量子化系统构造渐近对称群共伴随轨道的量子模，应用于 Virasoro 和 BMS$_3$ 群，推导常数轨道模并计算特征标，与几何作用路径积分结果一致。
中文摘要 AI 辅助
在本文中，我们通过一圈阶的路径积分量子化，为渐近对称群的共伴随轨道相关的量子模提供了一种系统构造。特别地，对于哈密顿量从下方无界的轨道，我们证明了适当选择积分轮廓可以定义一个收敛的欧几里得半线路径积分。与轨道关联的参考态由相应共伴随轨道上几何作用的路径积分确定。因此，共伴随模由参考态及其后代展开。我们将此形式应用于 Virasoro 和 BMS$_3$ 群，并推导出所有常数轨道对应的共伴随模。我们还通过计算模内的态数，计算了所有常数 Virasoro 和 BMS$_3$ 共伴随轨道的特征标，结果与具有周期欧几里得方向的几何作用路径积分的相应计算一致。
英文摘要
In this paper, we provide a systematic construction of quantum modules associated with coadjoint orbits of asymptotic symmetry groups through the path integral quantization at one-loop order. In particular, for the orbits with Hamiltonians unbounded from below, we show that an appropriate choice of integration contour defines a convergent Euclidean half-line path integral. The reference state associate with the orbit is determined by the path integral of the geometric action on the corresponding coadjoint orbit. The coadjoint module is therefore spanned by the reference state and its descendants. We apply this formalism to the Virasoro and BMS$_3$ groups and derive the coadjoint modules corresponding to all constant orbits. We also compute the characters of all constant Virasoro and BMS$_3$ coadjoint orbits by counting the states within the modules, and the results agree with the corresponding computations from the path integral of the geometric action with a periodic Euclidean direction.
发表机构
- Center for Joint Quantum Studies, Department of Physics, School of Science, Tianjin University（天津大学理学院物理系联合量子研究中心）
- School of Physics, Peking University（北京大学物理学院）
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