Noncommutative Quantum Mechanics on a Curved Space

M. Nakamura

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arXiv · 1503.06541

Noncommutative Quantum Mechanics on a Curved Space

M. Nakamura

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Abstract

Starting with the first-order singular Lagrangian, the canonical structures of the noncommutative quantum system on a submanifold embedded in the higher-dimensional Euclidean space are investigated with the projection operator method (POM) and the Dirac-bracket formulation in the case of the derivative-type constraint. Using the successive projection procedure and the iterativity of the Dirac bracket, the noncommutative quantum system is constructed in the form including all orders of the noncommutativity-parameters. When the noncommutative quantum system is constrained to a curved space, the commutator algebra of the system is presented within the 1st-order approximation with respect to Dirac-const. and the noncommutativity-parameters.

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M. Nakamura. 2015-03-23. Noncommutative Quantum Mechanics on a Curved Space. https://arxiv.org/abs/1503.06541

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