Non-Hermitian ${\cal PT}$-Symmetric Dirac-Pauli Hamiltonians with Real Energy Eigenvalues in the Magnetic Field

TL;DR

This paper derives exact energy spectra for non-Hermitian ${ m PT}$-symmetric Dirac-Pauli Hamiltonians with magnetic fields, highlighting potential experimental signatures of new particles predicted by the model.

Contribution

It introduces a ${ m PT}$-symmetric extension of Dirac-Pauli Hamiltonians using ${ m \

Findings

Exact energy spectra for fermions in magnetic fields without perturbation.

Discussion of experimental methods to detect properties of new particles.

Potential realization of ${ m PT}$-symmetric quantum systems in particle physics.

Abstract

The modified Dirac-Pauli equations, which is entered by means of ${\gamma_5}$-mass extension of Hamiltonian operators, are considered. We also take into account the interaction of fermions with the intensive homogenous magnetic field focusing attention on (g-2) gyromagnetic factor of particles with spin $1/2$. Without the use of perturbation theory in the external field the exact energy spectra are deduced with regard to spin effects of fermions. We discuss the possible proposals of experimental measuring of properties of new particles which arising in this model.