Dirac and Klein-Gordon particles in complex Coulombic fields; a similarity transformation

TL;DR

This paper explores non-Hermitian Dirac and Klein-Gordon Hamiltonians with complex Coulombic potentials, emphasizing that real, discrete spectra can exist without Hermiticity, using similarity transformations.

Contribution

It demonstrates that real spectra in non-Hermitian relativistic quantum systems can be achieved through similarity transformations, challenging the Hermiticity requirement.

Findings

Real spectra can exist in non-Hermitian Dirac and Klein-Gordon Hamiltonians.

Complex Coulombic potentials do not necessarily lead to complex eigenvalues.

Similarity transformations can relate non-Hermitian Hamiltonians to Hermitian counterparts.

Abstract

The observation that the existance of the amazing reality and discreteness of the spectrum need not be attributed to the Hermiticity of the Hamiltonian is reemphasized in the context of the non-Hermitian Dirac and Klein-Gordon Hamiltonians. Complex Coulombic potentials are considered.