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

Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3562510· OSTI ID:21501280

Castro, P G ^[1]; Chakraborty, B ^[2]; Kullock, R; Toppan, F ^[3]

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1. DM/ICE/UFJF, Campus Universitario, cep 36036-330, Juiz de Fora (Brazil)
2. S. N. Bose National Center for Basic Sciences, JD Block, Sector III, Salt-Lake, Kolkata-700098 (India)
3. TEO/CBPF, Rua Dr. Xavier Sigaud 150, cep 22290-180, Rio de Janeiro (RJ) (Brazil)

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 the quantization possible are solved. The spectrum of the single-particle Hamiltonians is computed. The multiparticle 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.

• OSTI ID: 21501280
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 52; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
COMMUTATION RELATIONS
ELECTRONIC EQUIPMENT
EQUIPMENT
HAMILTONIANS
HARMONIC OSCILLATORS
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
OSCILLATORS
QUANTIZATION
QUANTUM MECHANICS
QUANTUM OPERATORS
ROTATIONAL INVARIANCE
SYMMETRY
SYMMETRY GROUPS