su(1,1) Algebraic approach of the Dirac equation with Coulomb-type scalar and vector potentials in D + 1 dimensions

TL;DR

This paper employs an su(1,1) algebraic method to analyze the Dirac equation with Coulomb-type potentials in higher dimensions, deriving energy spectra and ground states through algebraic and supersymmetric techniques.

Contribution

It introduces an algebraic framework using su(1,1) Lie algebra for solving the Dirac equation with Coulomb potentials in D+1 dimensions, connecting algebraic and analytical results.

Findings

Derived energy spectrum using su(1,1) algebraic approach.

Obtained supersymmetric ground state solutions.

Reduced results to known analytical solutions in special cases.

Abstract

We study the Dirac equation with Coulomb-type vector and scalar potentials in D + 1 dimensions from an su(1, 1) algebraic approach. The generators of this algebra are constructed by using the Schr\"odinger factorization. The theory of unitary representations for the su(1, 1) Lie algebra allows us to obtain the energy spectrum and the supersymmetric ground state. For the cases where there exists either scalar or vector potential our results are reduced to those obtained by analytical techniques.