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Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation

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arxiv 1012.5158 v2 pith:TSWRMRID submitted 2010-12-23 hep-th math-phmath.MP

P. G. Castro , B. Chakraborty , R. Kullock , F. Toppan This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords algebrahopfinvariancedeformationhamiltoniansnoncommutativeoscillatorsrotational
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Noncommutative oscillators are first-quantized through an abelian Drinfel'd twist deformation of a Hopf algebra and its action on a module. Several important and subtle issues making possible the quantization are solved. The spectrum of the single-particle Hamiltonians is computed. The multi-particle Hamiltonians are fixed, unambiguously, by the Hopf algebra coproduct. The symmetry under particle exchange is guaranteed. In d=2 dimensions the rotational invariance is preserved, while in d=3 the so(3) rotational invariance is broken down to an so(2) invariance.

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