Lagrangian Aspects of Quantum Dynamics on a Noncommutative Space

Details Lagrangian Aspects of Quantum Dynamics on a Noncommutative Space Lagrangian Aspects of Quantum Dynamics on a Noncommutative Space

2003-02-20

arxiv.org/abs/hep-th/0302167v2

Physics

High Energy Physics

High Energy Physics - Theory

15 pages, references added, minor corrections, to be published in the Proceedings of the Workshop "Contemporary Geometry and R

Scientific paper

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.

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