Noncommutative Quantum Mechanics on a Curved Space
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.
Cite
@article{arxiv.1503.06541,
title = {Noncommutative Quantum Mechanics on a Curved Space},
author = {M. Nakamura},
journal= {arXiv preprint arXiv:1503.06541},
year = {2015}
}
Comments
17 pages, 13 references