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Teoreticheskaya i Matematicheskaya Fizika, 2004, Volume 140, Number 3, Pages 480–491
DOI: https://doi.org/10.4213/tmf100
(Mi tmf100)
 

This article is cited in 19 scientific papers (total in 19 papers)

Path Integrals in Noncommutative Quantum Mechanics

B. G. Dragovich, Z. Rakić

University of Belgrade
References:
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.
Received: 05.11.2003
Revised: 12.01.2004
English version:
Theoretical and Mathematical Physics, 2004, Volume 140, Issue 3, Pages 1299–1308
DOI: https://doi.org/10.1023/B:TAMP.0000039834.84359.f8
Bibliographic databases:
Language: Russian
Citation: B. G. Dragovich, Z. Rakić, “Path Integrals in Noncommutative Quantum Mechanics”, TMF, 140:3 (2004), 480–491; Theoret. and Math. Phys., 140:3 (2004), 1299–1308
Citation in format AMSBIB
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\paper Path Integrals in Noncommutative Quantum Mechanics
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\transl
\jour Theoret. and Math. Phys.
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\vol 140
\issue 3
\pages 1299--1308
\crossref{https://doi.org/10.1023/B:TAMP.0000039834.84359.f8}
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Linking options:
  • https://www.mathnet.ru/eng/tmf100
  • https://doi.org/10.4213/tmf100
  • https://www.mathnet.ru/eng/tmf/v140/i3/p480
  • This publication is cited in the following 19 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Теоретическая и математическая физика Theoretical and Mathematical Physics
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