Exact Solutions for Non-Hermitian Dirac-Pauli Equation in an intensive magnetic field

TL;DR

This paper derives exact solutions for the non-Hermitian Dirac-Pauli equation in strong magnetic fields, exploring unbroken PT symmetry regions and potential experimental implications for maximal mass limits of elementary particles.

Contribution

It develops methods to find exact energy spectra of non-Hermitian Dirac-Pauli equations without perturbation theory, considering fermion interactions with intense magnetic fields and PT symmetry.

Findings

Exact energy spectra derived without perturbation theory

Identification of unbroken PT symmetry regions in non-Hermitian Hamiltonians

Discussion of experimental observability related to maximal mass conjecture

Abstract

The modified Dirac-Pauli equations, which are introduced by means of ${\gamma_5}$-mass factorization of the ordinary Klein-Gordon operator, are considered. We also take into account the interaction of fermions with the intensive homogenous magnetic field focusing attention to their (g-2) gyromagnetic factor. The basis of this approach is developing of methods for study of the structure of regions of unbroken $\cal PT$ symmetry of Non-Hermitian Hamiltonians which be no studied earlier. For that, without the use of perturbation theory in the external field the exact energy spectra are deduced with regard to spin effects of fermions. We also investigate the unique possible of experimental observability the non-Hermitian restrictions in the spectrum of mass consistent with the conjecture Markov about Maximal Mass. This, in principal will may allow to find out the existence of an upper limit value in spectrum masses of elementary particles and confirm or deny the significance of the Planck mass.