Exact solutions for non-Hermitian Dirac-Pauli equation in an intensive magnetic field

Abstract

The modified Dirac-Pauli equations, which are introduced by means of γ 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 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.

Non-Hermitian quantum theory with maximal mass

“…Taking into account the quantum electrodynamic contribution into the anomalous magnetic moment of the electron to e 2 , we have Δμ = α 2π μ 0 , where α = e 2 = 1/137 is the fine structure constant, and it is still assumed that the external field potential satisfies the free Maxwell equation. As it was shown in paper [45], [48], with the help of the modified Dirac-Pauli equation we can find the exact values of the energy spectrum for the Hamiltonian (21),…”

“…Also the eigenvalues and eigenvectors for free modified Dirac Hamiltonian were found [40], [43], [44]. The law of the current density continuity was obtained [45].…”

Non-Hermitian $$\mathcal{PT}$$ PT -Symmetric Relativistic Quantum Theory in an Intensive Magnetic Field

“…With it really is hard not to agree because the interactions of ordinary neutrinos with the electromagnetic fields are extremely weak. However if one to suggest using the "exotic neutrinos" the interaction with magnetic field may be really significantly increased thanks to the coefficient which be equal to the ratio of maximal mass and mass of neutrinos k = M/m ν [12], [13]. Such experiments in our opinion may be very fruitful for creation the new physics beyond the SM.…”

“…It is shown by us that there is a constraint on the parameter m in the algebraic theory. In this case, there are reasons to believe that a direct relationship exists between M obtained by algebraic way and M which is consequence the geometric approach to modified QFT with the fundamental mass [3], [4].…”

An algebraic PT-symmetric quantum theory with a maximal mass

“…Thus, experiments on the search of "exotic" particles may result in detection of existence of the limiting mass. This approach becomes realistic due to the calculation of the energy spectrum of a neutral fermion possessing an anomalous magnetic moment in the theory with a maximal mass [3,4]. Thus, further development of the theory founded by Kadyshevsky can and should yield proposals on formulation of such experiments in the near future.…”