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Explicit path integration is carried out for the Green's functions of specialrelativistic harmonic oscillators in (1+1)- and (3+1)-dimensional Minkowskispace-time modeled by a Klein-Gordon particle in the universal coveringspace-time of the anti-de Sitter static space-time. The energy spectrumtogether with the normalized wave functions are obtained. In thenon-relativistic limit, the bound states of the one- and three-dimensionalordinary oscillators are regained.Comment: 23 pages, no figures. Accepted for publication in Eur.Phys.J.

Path integral for relativistic oscillators: model of the Klein-Gordon particle in AdS space