Geodesic
Path Integrals in Noncommutative Quantum Mechanics
Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 3, pp. 480-491 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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B. G. Dragovich; Z. Rakić. Path Integrals in Noncommutative Quantum Mechanics. Teoretičeskaâ i matematičeskaâ fizika, Tome 140 (2004) no. 3, pp. 480-491. http://geodesic.mathdoc.fr/item/TMF_2004_140_3_a8/

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