Coherent states for the two-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field

TL;DR

This paper develops an algebraic approach using $SU(1,1)$ group theory to analyze the 2D Dirac-Moshinsky oscillator in a magnetic field, deriving energy spectra, eigenfunctions, and coherent states.

Contribution

It introduces a novel algebraic method employing $SU(1,1)$ group theory to solve and construct coherent states for the 2D Dirac-Moshinsky oscillator in a magnetic field.

Findings

Energy spectrum derived analytically

Eigenfunctions explicitly constructed

Relativistic coherent states obtained in closed form

Abstract

We show that the $(2+1)$-dimensional Dirac-Moshinsky oscillator coupled to an external magnetic field can be treated algebraically with the $SU(1,1)$ group theory and its group basis. We use the $su(1,1)$ irreducible representation theory to find the energy spectrum and the eigenfunctions. Also, with the $su(1,1)$ group basis we construct the relativistic coherent states in a closed form for this problem.