Algebraic solution and coherent states for the Dirac oscillator interacting with a topological defect

TL;DR

This paper provides exact solutions for the Dirac oscillator in various topological defect spacetimes, revealing an underlying SU(1,1) symmetry, and constructs coherent states with their dynamics.

Contribution

It introduces an algebraic method to solve the Dirac oscillator with topological defects and derives explicit wave functions, spectra, and coherent states.

Findings

Exact energy spectra for the Dirac oscillator in different topological defects.

Identification of SU(1,1) symmetry in the radial problem.

Construction and analysis of radial coherent states and their evolution.

Abstract

In this work we study and exactly solve the Dirac oscillator with three different topological defects, namely the cosmic string spacetime ($\Lambda_\mp$), the magnetic cosmic string spacetime ($\Theta_\mp$) and the cosmic dislocation spacetime ($\Pi_\mp$). Moreover, we show that the radial part of this problem possess an $SU(1,1)$ symmetry. From this, we obtain the wave functions and their respective energy spectrum by means of the Schr\"odinger factorization. Also, we compute the radial coherent states of the eigenfunctions of each problem and their time evolution.