On a dynamical symmetry group of the relativistic linear singular oscillator

TL;DR

This paper presents an exact factorization method for the relativistic linear singular oscillator, revealing its underlying $SU(1,1)$ Lie algebra structure through finite-difference operators.

Contribution

It introduces finite-difference raising and lowering operators that form an $SU(1,1)$ algebra, providing a new algebraic framework for the relativistic oscillator.

Findings

Finite-difference operators form an $SU(1,1)$ Lie algebra.

Exact factorization of the relativistic oscillator achieved.

New algebraic tools for analyzing relativistic quantum systems.

Abstract

An exact approach for the factorization of the relativistic linear singular oscillator is proposed. This model is expressed by the finite-difference Schr\"odinger-like equation. We have found finite-difference raising and lowering operators, which are with the Hamiltonian operator form the close Lie algebra of the $SU(1, 1)$ group.