0000000000013942

AUTHOR

Zhi-cheng Lu

showing 2 related works from this author

From where do quantum groups come?

1993

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.

Quantization (physics)POVMCanonical quantizationQuantum processPhase spaceQuantum mechanicsQuantum operationGeneral Physics and AstronomyQuantum phasesGroup theoryMathematicsFoundations of Physics
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Remarks on quantum groups

1991

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.

Poisson bracketTheoretical physicsToy modelQuantum groupPhase spaceComplex systemStatistical and Nonlinear PhysicsMeaning (non-linguistic)QuantumRealization (systems)Mathematical PhysicsMathematicsMathematical physicsLetters in Mathematical Physics
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