Path integral for relativistic oscillators: model of the Klein-Gordon particle in AdS space
arXiv:quant-ph/0210101 · doi:10.1140/epjc/s2003-01164-x
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.
23 pages, no figures. Accepted for publication in Eur.Phys.J.C