DOI: 10.1140/epjc/s2003-01164-x
Path integral for relativistic oscillators: model of the Klein-Gordon particle in AdS space
M.T. Chefrour1, F. Benamira2 and L. Guechi21 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 )
Abstract
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
