Lagrangian Aspects of Quantum Dynamics on a Noncommutative Space
Abstract
Description
In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with noncommutative coordinates is equivalent to another one with commutative coordinates. We found connection between quadratic classical Lagrangians of these two systems. We also shown that there is a subclass of quadratic Lagrangians, which includes harmonic oscillator and particle in a constant field, whose connection between ordinary and noncommutative regimes can be expressed as a linear change of position in terms of a new position and velocity.
15 pages, references added, minor corrections, to be published in the Proceedings of the Workshop "Contemporary Geometry and Related Topics", (Belgrade, 2002)
15 pages, references added, minor corrections, to be published in the Proceedings of the Workshop "Contemporary Geometry and Related Topics", (Belgrade, 2002)