Authors: Dragović, Branko 
Rakić, Zoran
Title: Path integrals in noncommutative quantum mechanics
Journal: Theoretical and Mathematical Physics
Volume: 140
Issue: 3
First page: 1299
Last page: 1308
Issue Date: 1-Jan-2004
Rank: M23
ISSN: 0040-5779
DOI: 10.1023/B:TAMP.0000039834.84359.f8
Abstract: 
We consider an extension of the Feynman path integral to the quantum mechanics of noncommuting spatial coordinates and formulate the corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians). The basis of our approach is that a quantum mechanical system with a noncommutative configuration space can be regarded as another effective system with commuting spatial coordinates. Because the path integral for quadratic Lagrangians is exactly solvable and a general formula for the probability amplitude exists, we restrict our research to this class of Lagrangians. We find a general relation between quadratic Lagrangians in their commutative and noncommutative regimes and present the corresponding noncommutative path integral. This method is illustrated with two quantum mechanical systems in the noncommutative plane: a particle in a constant field and a harmonic oscillator.
Keywords: Feynman path integral | noncommutative quantum mechanics | systems with quadratic Lagrangians

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