Path Integral Approach to Noncommutative Quantum Mechanics
Abstract
Description
We consider Feynman's path integral approach to quantum mechanics with a noncommutativity in position and momentum sectors of the phase space. We show that a quantum-mechanical system with this kind of noncommutativity is equivalent to the another one with usual commutative coordinates and momenta. We found connection between quadratic classical Hamiltonians, as well as Lagrangians, in their commutative and noncommutative regimes. The general procedure to compute Feynman's path integral on this noncommutative phase space with quadratic Lagrangians (Hamiltonians) is presented. Using this approach, a particle in a constant field, ordinary and inverted harmonic oscillators are elaborated in detail.
11 pages, to appear in the proceedings of the Fifth Int. Workshop "Lie Theory and its Applications in Physics" (Varna, 2003), World Scientific, 2004
11 pages, to appear in the proceedings of the Fifth Int. Workshop "Lie Theory and its Applications in Physics" (Varna, 2003), World Scientific, 2004