Path integral for relativistic oscillators: model of the Klein-Gordon particle in AdS spaceM.T. Chefrour1, F. Benamira2 and L. Guechi2
1 Département de Physique, Faculté des Sciences, Université Badji Mokhtar, Annaba, Algeria
2 Laboratoire de Physique Théorique, Département de Physique, Faculté des Sciences, Université Mentouri, Route d'Ain El Bey, Constantine, Algeria
(Received: 29 June 2002 / Revised version: 3 February 2003 / Published online: 24 March 2003 )
Explicit path integration is carried out for the Green's functions of special relativistic harmonic oscillators in ( 1+1)- and ( 3+1 )-dimensional Minkowski space-time modeled by a Klein-Gordon particle in the universal covering space-time of the anti-de Sitter static space-time. The energy spectrum together with the normalized wave functions are obtained. In the non-relativistic limit, the bound states of the one- and three-dimensional ordinary oscillators are regained.
© Società Italiana di Fisica, Springer-Verlag 2003