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2009

Position-dependent noncommutativity in quantum mechanics

Gomes, M., Kupriyanov, V. G.

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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.

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