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arXiv · 0902.3252

Position-dependent noncommutativity in quantum mechanics

M. Gomes·V. G. Kupriyanov
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Abstract

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}]=ω^{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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M. Gomes, V. G. Kupriyanov. 2009-06-15. Position-dependent noncommutativity in quantum mechanics. https://doi.org/10.1103/physrevd.79.125011

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