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

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.