The symmetry groups of noncommutative quantum mechanics and coherent state quantization

Journal Article · Fri Mar 15 04:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4793992· OSTI ID:22162816

Chowdhury, S. Hasibul Hassan; Ali, S. Twareque ^[1]

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1. Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8 (Canada)

We explore the group theoretical underpinning of noncommutative quantum mechanics for a system moving on the two-dimensional plane. We show that the pertinent groups for the system are the two-fold central extension of the Galilei group in (2+1)-space-time dimensions and the two-fold extension of the group of translations of R{sup 4}. This latter group is just the standard Weyl-Heisenberg group of standard quantum mechanics with an additional central extension. We also look at a further extension of this group and discuss its significance to noncommutative quantum mechanics. We build unitary irreducible representations of these various groups and construct the associated families of coherent states. A coherent state quantization of the underlying phase space is then carried out, which is shown to lead to exactly the same commutation relations as usually postulated for this model of noncommutative quantum mechanics.

• OSTI ID: 22162816
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 54; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANNIHILATION OPERATORS
COMMUTATION RELATIONS
CONFIGURATION
EIGENSTATES
GROUP THEORY
IRREDUCIBLE REPRESENTATIONS
PHASE SPACE
QUANTIZATION
QUANTUM MECHANICS
SPACE-TIME
SYMMETRY GROUPS
THREE-DIMENSIONAL CALCULATIONS