Authors: Dragović, Branko
Rakić, Zoran
Title: Noncommutative classical and quantum mechanics for quadratic Lagrangians (Hamiltonians)
Journal: Proceedings of the Steklov Institute of Mathematics
Volume: 265
Issue: 1
First page: 82
Last page: 91
Issue Date: 22-Oct-2009
ISSN: 00815438
DOI: 10.1134/S0081543809020072
Classical and quantum mechanics based on an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by a linear transformation of coordinates and transferred to the Hamiltonian (Lagrangian). This linear transformation does not change the quadratic form of the Hamiltonian (Lagrangian), and Feynman's path integral preserves its exact expression for quadratic models. The compact general formalism presented here can be easily illustrated in any particular quadratic case. As an important result of phenomenological interest, we give the path integral for a charged particle in the noncommutative plane with a perpendicular magnetic field. We also present an effective Planck constant h{stroke}eff which depends on additional noncommutativity. © Pleiades Publishing, Ltd., 2009.

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