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Non-Hermitian \(\mathcal {P}\mathcal {T}\)-Symmetric Dirac-Pauli Hamiltonians with Real Energy Eigenvalues in the Magnetic Field

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Abstract

The modified Dirac-Pauli equations, which is entered by means of γ 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.

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Notes

  1. As the exotic particles do not agree in the “flat limit” with the ordinary Dirac expressions then one can assume that in this case we deal with a description of some new particles, properties of which have not yet been studied. This fact for the first time has been fixed by V.G.Kadyshevsky in his early works in the geometric approach to the development of the quantum field theory with a fundamental mass” Ref. [3033] in curved de-Sitter momentum space. Besides in Ref. [34, 35] it was noted that the most intriguing prediction of the new approach is the possible existence of exotic fermions with no analogues in the SM, which may be candidates for constituents of dark matter .

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Acknowledgments

We are grateful to Prof. V.G. Kadyshevsky (who is no longer with us) for fruitful and highly useful discussions.

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Correspondence to V. N. Rodionov.

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Rodionov, V.N. Non-Hermitian \(\mathcal {P}\mathcal {T}\)-Symmetric Dirac-Pauli Hamiltonians with Real Energy Eigenvalues in the Magnetic Field. Int J Theor Phys 54, 3907–3919 (2015). https://doi.org/10.1007/s10773-014-2410-4

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