标题： 双曲面上的粒子动力学与 SO(1,N) 群的酉表示 显示英文标题

标题： Particle dynamics on hyperboloid and unitary representation of SO(1,N) group

摘要： 我们分析了粒子在嵌入$N+1$维闵可夫斯基空间的$N$维单叶双曲面上的动力学。 由时空$SO_\uparrow (1,N)$对称性构造的动力学积分被用于规范不变的哈密顿约化。 物理相空间参数化了双曲面上所有经典轨迹的集合。 在量子情形下，通过对渐近变量的变换解决了对称生成元的算符排序问题。 正则量子化导致在希尔伯特空间$L^2(S^{N-1})$上的$SO_\uparrow (1,N)$群的酉不可约表示。 显示英文摘要

摘要： We analyze particle dynamics on $N$ dimensional one-sheet hyperboloid embedded in $N+1$ dimensional Minkowski space. The dynamical integrals constructed by $SO_\uparrow (1,N)$ symmetry of spacetime are used for the gauge-invariant Hamiltonian reduction. The physical phase-space parametrizes the set of all classical trajectories on the hyperboloid. In quantum case the operator ordering problem for the symmetry generators is solved by transformation to asymptotic variables. Canonical quantization leads to unitary irreducible representation of $SO_\uparrow (1,N)$ group on Hilbert space $L^2(S^{N-1})$.