Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation
High Energy Physics - Theory
2011-05-05 v2 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1012.5158,
title = {Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation},
author = {P. G. Castro and B. Chakraborty and R. Kullock and F. Toppan},
journal= {arXiv preprint arXiv:1012.5158},
year = {2011}
}
Comments
21 pages, references added