The Operator Algebra of the Quantum Relativistic Oscillator

Details The Operator Algebra of the Quantum Relativistic Oscillator The Operator Algebra of the Quantum Relativistic Oscillator

1997-05-12

arxiv.org/abs/physics/9705012v1

Physics

Mathematical Physics

14 pages, Latex

Scientific paper

10.1063/1.532148

The operator algebras of a new family of relativistic geometric models of the relativistic oscillator are studied. It is shown that, generally, the operator of number of quanta and the pair of the shift operators of each model are the generators of a non-unitary representation of the $so(1,2)$ algebra, except a special case when this algebra becomes the standard one of the non-relativistic harmonic oscillator.

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