Pseudospin and spin symmetries in 1+1 dimensions: The case of the Coulomb potential

TL;DR

This paper investigates fermions in 1+1 dimensions with Coulomb potentials, analyzing spin and pseudospin symmetries, bound states, and transformations, with implications extendable to 3+1 dimensions.

Contribution

It provides a comprehensive analysis of spin and pseudospin symmetries in 1+1 dimensions with Coulomb potentials, including all potential sign configurations and their bound-state solutions.

Findings

Bound-state solutions depend on potential signs and configurations.

Charge-conjugation and chiral transformations relate spin and pseudospin symmetries.

Results generalize previous specific cases and extend to higher dimensions.

Abstract

The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. We show the relation between spin and pseudospin symmetries by means of charge-conjugation and $\gamma^{5}$ chiral transformations. The cases of pure pseudoscalar and mixed vector-scalar potentials, already analyzed in previous works, are obtained as particular cases. The results presented can be extended to 3+1 dimensions.