Noncommutative classical and quantum mechanics for quadratic Lagrangians (Hamiltonians) |
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Authors: | Branko Dragovich Zoran Rakić |
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Institution: | (1) Institute of Physics, P.O. Box 57, 11001 Belgrade, Serbia;(2) Faculty of Mathematics, University of Belgrade, P.O. Box 550, 11001 Belgrade, Serbia |
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Abstract: | 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 ħ
eff which depends on additional noncommutativity. |
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Keywords: | |
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