Position-dependent noncommutativity in quantum mechanics
Mathematical Physics
2009-06-15 v2 High Energy Physics - Theory
math.MP
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}]=\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.
Cite
@article{arxiv.0902.3252,
title = {Position-dependent noncommutativity in quantum mechanics},
author = {M. Gomes and V. G. Kupriyanov},
journal= {arXiv preprint arXiv:0902.3252},
year = {2009}
}
Comments
published version, references added