Physics NotePublished
Noncommutative oscillators from a Hopf algebra twist deformation. A first principles derivation.
Ricardo Kullock; P. G. Castro; B. Chakraborty
Publication details
- Authors
- Ricardo Kullock; P. G. Castro; B. Chakraborty
- Type
- Physics Note
- Status
- Published
- Publication date
- 26/01/2011
- Description
- 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.
- Year
- 2010
- Number
- CBPF-NF-003/10
- Linked to a thesis
- No
- Linked to a grant
- No