Special-relativistic harmonic oscillator modeled by Klein-Gordon theory in anti-de Sitter space

It is shown that the one-particle sector of the Klein-Gordon theory in the universal covering space of the anti-de Sitter space (CAdS) can be interpreted, in a natural way, as a special-relativistic oscillator in Minkowski space. The quantum wave functions have a significantly different behavior with respect to the nonrelativistic ones. The energy spectrum coincides, up to the ground state energy, with that of the nonrelativistic oscillator. The requirement of having the adequate nonrelativistic limit for the special-relativistic oscillator theory turns out to be equivalent to the imposition of the Dirichlet-type boundary condition at spatial infinity on CAdS Klein-Gordon functions. (C) 1996 American Institute of Physics.