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


Starting with the modified Dirac equations for free massive particles with the γ5-extension of the physical mass \(m\to m_1+\gamma_5m_2\), we consider equations of relativistic quantum mechanics in the presence of an external electromagnetic field. The new approach is developing on the basis of existing methods for study the unbroken PT symmetry of Non-Hermitian Hamiltonians. The paper shows that this modified model contains the definition of the mass parameter, which may use as the determination of the magnitude scaling of energy M. Obviously that the transition to the standard approach is valid when small in comparison with M energies and momenta. Formally, this limit is performed when \(M\to\infty\), which simultaneously should correspond to the transition to a Hermitian limit \(m2\to0\). Inequality \(m\leq M\) may be considered and as the restriction of the mass spectrum of fermions considered in the model. Within of this approach, the effects of possible observability mass parameters: \(m_1, m_2, M\) are investigated taking into account the interaction of the magnetic field with charged fermions together with the accounting of their anomalous magnetic moments.
High Energy Physics – Theory (hep-th); High Energy Physics – Phenomenology (hep-ph); Mathematical Physics (math-ph); Quantum Physics (quant-ph)

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