Position-dependent noncommutativity in quantum mechanics

Journal Article · Mon Jun 15 00:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.79.125011· OSTI ID:21301018

Gomes, M; Kupriyanov, V G ^[1]

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1. Instituto de Fisica, Universidade de Sao Paulo (Brazil)

The model of the position-dependent noncommutativity in quantum mechanics is proposed. We start with given commutation relations between the operators of coordinates [x-circumflex{sup i},x-circumflex{sup j}]={omega}{sup ij}(x-circumflex), and construct the complete algebra of commutation relations, including the operators of momenta. The constructed algebra is a deformation of a standard Heisenberg algebra and obeys the Jacobi identity. The key point of our construction is a proposed first-order Lagrangian, which after quantization reproduces the desired commutation relations. Also we study the possibility to localize the noncommutativity.

• OSTI ID: 21301018
• Journal Information: Physical Review. D, Particles Fields, Vol. 79, Issue 12; Other Information: DOI: 10.1103/PhysRevD.79.125011; (c) 2009 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMMUTATION RELATIONS
CONSTRUCTION
COORDINATES
DEFORMATION
LAGRANGIAN FUNCTION
QUANTIZATION
QUANTUM MECHANICS