Dual families of noncommutative quantum systems

Journal Article · Fri Apr 15 04:00:00 EDT 2005 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.71.085005· OSTI ID:20709109

Scholtz, Frederik G; Chakraborty, Biswajit; Gangopadhyay, Sunandan; Hazra, Arindam Ghosh ^[1]

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1. Institute of Theoretical Physics, University of Stellenbosch, Private Bag X1, Matieland 7602 (South Africa)

We demonstrate how a one parameter family of interacting noncommuting Hamiltonians, which are physically equivalent, can be constructed in noncommutative quantum mechanics. This construction is carried out exactly (to all orders in the noncommutative parameter) and analytically in two dimensions for a free particle and a harmonic oscillator moving in a constant magnetic field. We discuss the significance of the Seiberg-Witten map in this context. It is shown for the harmonic oscillator potential that an approximate duality, valid in the low-energy sector, can be constructed between the interacting commutative and a noninteracting noncommutative Hamiltonian. This approximation holds to order 1/B and is therefore valid in the case of strong magnetic fields and weak Landau-level mixing.

• OSTI ID: 20709109
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 71; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
COMMUTATION RELATIONS
DUALITY
HAMILTONIANS
HARMONIC OSCILLATORS
MAGNETIC FIELDS
POTENTIALS
QUANTUM FIELD THEORY
QUANTUM MECHANICS