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arXiv · 1012.5158

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

P. G. Castro·B. Chakraborty·R. Kullock·F. Toppan
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Abstract

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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P. G. Castro, B. Chakraborty, R. Kullock, F. Toppan. 2010-12-23. Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation. https://doi.org/10.1063/1.3562510

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