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Z. Naturforsch. 67a, 77 – 88
(2012)
doi:10.5560/ZNA.2011-0060
Relativistic Oscillators in a Noncommutative Space: a Path Integral Approach
1 Laboratoire LRPPS, Université de Kasdi Merbah-Ouargla, BP 511, Route Ghardaïa, 30000 Ouargla, Algérie (permanent address)
2 Laboratoire de Mathématiques, Informatique et Applications, Université de Haute-Alsace, 4 rue des Frères Lumière F-68093 Mulhouse, France
3 Laboratoire (L.S.D.C), Département des Sciences de la Matière, Faculté des Sciences Exactes et Sciences de la Vie, Université de Oum El Bouaghi, 04000 Oum El Bouaghi, Algérie
4 Laboratoire de Physique Théorique, Université de Jijel BP98 Ouled Aissa, 18000 Jijel, Algérie (permanent address)
5 Laboratoire de Physique Théorique, Université Paris-Sud 11, Bâtiment 210, Orsay Cedex France (visitor address)
Received January 11, 2011 / revised October 3, 2011
Reprint requests to: M. M.; E-mail:
meradm@gmail.com
In this paper, we consider the dynamics of Klein–Gordon and Dirac oscillators in (2 + 1) dimensions with noncommutativity of the spatial coordinates using the supersymmetric path integral formalism. The propagator is calculated and the energy eigenvalues with their corresponding eigenfunctions are deduced.
Key words: Noncommutative Geometry; Path Integral; Klein–Gordon and Dirac Oscillators.
PACS numbers: 03.65.Pm; 03.65.Ca; 03.65.Db; 03.65.Ge