The operator algebra of the quantum relativistic oscillator

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Abstract
The operator algebras of a new family of relativistic geometric models of the relativistic oscillator [I. I. Cotăescu, Int. J. Mod. Phys. A 12, 3545 (1997)] are studied. It is shown that, generally, the operator of number of quanta and the pair of shift operators of each model are the generators of a nonunitary representation of the so(1,2) algebra, except for a special case when this algebra becomes the standard of the nonrelativistic harmonic oscillator.
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