0000000000013942
AUTHOR
Zhi-cheng Lu
From where do quantum groups come?
The phase space realizations of quantum groups are discussed using *-products. We show that on phase space, quantum groups appear necessarily as two-parameter deformation structures, one parameter (v) being concerned with the quantization in phase space, the other (η) expressing the quantum groups as “deformation” of their Lie counterparts. Introducing a strong invariance condition, we show the uniqueness of the η-deformation. This suggests that the strong invariance condition is a possible origin of the quantum groups.
Remarks on quantum groups
We give a Poisson-bracket realization of SL q (2) in the phase space ℝ2. We then discuss the physical meaning of such a realization in terms of a modified (regularized) toy model, the nonregularized version of which is due to Klauder. Some general remarks and suggestions are also presented in this Letter.