标题： (2+1)-维引力中的运动常量与共形反德西特代数 显示英文标题

标题： Constants of motion and the conformal anti - de Sitter algebra in (2+1)-Dimensional Gravity

摘要： 对于具有拓扑结构 R × T² 和负宇宙常数的 2+1 维引力，计算了运动常量。它们的某些线性组合在 ADM 或平行度量变量下满足反德西特代数 so(2,2)。以平行度量参数表示时，量子化过程很简单。当包含哈密顿量时，可以推导出三个新的全局常量，并且量子代数扩展到共形代数 so(2,3)。模群作为共形群的一个离散子群出现，其量子作用由这些守恒量生成。 显示英文摘要

摘要： Constants of motion are calculated for 2+1 dimensional gravity with topology R x T^2 and negative cosmological constant. Certain linear combinations of them satisfy the anti - de Sitter algebra so(2,2) in either ADM or holonomy variables. Quantisation is straightforward in terms of the holonomy parameters. On inclusion of the Hamiltonian three new global constants are derived and the quantum algebra extends to that of the conformal algebra so(2,3). The modular group appears as a discrete subgroup of the conformal group. Its quantum action is generated by these conserved quantities.