Position-dependent noncommutativity in quantum mechanics

Details Position-dependent noncommutativity in quantum mechanics Position-dependent noncommutativity in quantum mechanics

2009-02-18

arxiv.org/abs/0902.3252v2

Phys. Rev. D 79, 125011 (2009)

Physics

Mathematical Physics

published version, references added

Scientific paper

10.1103/PhysRevD.79.125011

The model of the position-dependent noncommutativety in quantum mechanics is proposed. We start with a given commutation relations between the operators of coordinates [x^{i},x^{j}]=\omega^{ij}(x), 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 obey 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 noncommutativety.

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