【摘要】 通常所谓的量子包络代数可以在经典Poisson括号的意义下实现,以谐振子系统为例,给出U_q(SU(2))的这种经典实现,指出这种q变形伴随着相空间复坐标的Beltrami变形。并讨论了这种经典q变形谐振子系统的量子化,得到在Lie括号意义下的U_q(SU(2))代数。更多还原

【Abstract】 We point out that the usual quantum enveloping algebra can be realized at classical level in the sense of Poisson bracket. As an example, we give the classical realization of Uq(SU(2)) by a system of classical harmonic oscillators. We show that the q-deformation corresponds to Beltrami deformation of the complex coordinate of phase space, h quantization of the system of the classical deformed oscillators is also discussed, Uq(SU(2)) algebra in Lie bracket obtained.更多还原