2014/04/02 by V.N. Rodionov, V. N. Rodionov, Rodionov, V. N. · 2 citations
Mathematics · Physics and Astronomy · #Neutrino Physics Research #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #hep-ph #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1404.0503
26 pages, 3 figures. arXiv admin note: text overlap with arXiv:1309.0231
arxiv created 2014/04/02 · arxiv updated 2014/04/03
Starting with the modified Dirac equations for free massive particles with the γ5-extension of the physical mass m→ m1 + γ5 m2, 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 \cal 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→∞, which simultaneously should correspond to the transition to a Hermitian limitm2→ 0. Inequality m ≤ 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: m1, m2, M are investigated taking into account the interaction of the magnetic field with charged fermions together with the accounting of their anomalous magnetic moments.