Abstract
This paper concerns a relativistic model of a particle with internal structure: the quantum relativistic oscillator. We distinguish the nonrelativistic limit of the overall motion from the nonrelativistic limit of the internal structure. The latter limit is given in terms of a contraction between the algebra of SO(3,2) and that of the three-dimensional harmonic oscillator. We analyze this contraction process in detail and show that the quantum relativistic oscillator is the appropriate relativistic generalization of harmonic internal motion.
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