2003/02/20 by Branko Dragovich, Бранко Драгович, Dragovich, Branko +3
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Noncommutative and Quantum Gravity Theories #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.hep-th/0302167
15 pages, references added, minor corrections, to be published in the Proceedings of the Workshop "Contemporary Geometry and Related Topics", (Belgrade, 2002)
openalex publication_date 2003/02/20 · arxiv created 2003/07/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.