The Operator Algebra of the Quantum Relativistic Oscillator

Abstract

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.

14 pages, Latex

References in corpus (1)

• Geometric Models of the Relativistic Harmonic Oscillator

Cited by in corpus (3)

• The Dirac particle on de Sitter background
• Geometric models of (d+1)-dimensional relativistic rotating oscillators
• The leader operators of the $(d+1)$-dimensional relativistic rotating oscillators