Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime

TL;DR

This paper explores the algebraic structure and coherent states of a relativistic quantum particle in cosmic string spacetime with magnetic and scalar potentials, deriving energy spectra and eigenfunctions.

Contribution

It introduces an algebraic approach using $su(1,1)$ symmetry to solve the relativistic quantum problem in cosmic string spacetime, including explicit coherent states.

Findings

Energy spectrum and eigenfunctions derived algebraically

Explicit form of relativistic coherent states provided

Identification of $su(1,1)$ symmetry in the problem

Abstract

We study a relativistic quantum particle in cosmic string spacetime in the presence of a uniform magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the $su(1,1)$ symmetry. We obtain the energy spectrum and eigenfunctions of this problem by using two algebraic methods: the Schr\"odinger factorization and the tilting transformation. Finally, we give the explicit form of the relativistic coherent states for this problem.