So (2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation

TL;DR

This paper explores the (1+1)-dimensional position-dependent mass Dirac equation using so(2,1) potential algebra, analyzing effects of a spatially varying Fermi velocity and pseudoscalar potential through point canonical transformations.

Contribution

It introduces a novel approach to solving the Dirac equation with position-dependent mass and Fermi velocity using algebraic methods and canonical transformations.

Findings

Derived solutions for the Dirac equation with position-dependent parameters

Analyzed effects of pseudoscalar potential on solutions

Established a framework for algebraic treatment of such systems

Abstract

We investigate the (1+1)-dimensional position-dependent mass Dirac equation within the confines of so(2,1) potential algebra by utilizing the character of a spatial varying Fermi velocity. We examine the combined effects of the two when the Dirac equation is equipped with an external pseuodoscalar potential. Solutions of the three cases induced by so(2, 1) are explored by profitably making use of a point canonical transformation.