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Starting with the modified Dirac equations for free massive particles withthe $\gamma_5$-extension of the physical mass $m\rightarrow m_1 + \gamma_5m_2$, we consider equations of relativistic quantum mechanics in the presenceof an external electromagnetic field. The new approach is developing on thebasis of existing methods for study the unbroken $\cal PT$ symmetry ofNon-Hermitian Hamiltonians. The paper shows that this modified model containsthe definition of the mass parameter, which may use as the determination of themagnitude scaling of energy $M$. Obviously that the transition to the standardapproach is valid when small in comparison with $M$ energies and momenta.Formally, this limit is performed when $M\rightarrow\infty$, whichsimultaneously should correspond to the transition to a \emph{Hermitianlimit}$m_2\rightarrow 0$. Inequality $m \leq M$ may be considered and as therestriction of the mass spectrum of fermions considered in the model. Within ofthis approach, the effects of possible \emph{observability} mass parameters:$m_1, m_2$, $M$ are investigated taking into account the interaction of themagnetic field with charged fermions together with the accounting of theiranomalous magnetic moments.

Non-Hermitian $\cal PT$-symmetric relativistic Quantum mechanics with a maximal mass in an external magnetic field