Abstract. A geometric interpretation of the spontaneous symmetry breaking effect, which plays a key role in the Standard Model, is developed. The advocated approach is related to the effective use of the momentum 4-spaces of the constant curvature, de Sitter and anti de Sitter, in the apparatus of quantum field theory.

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.

A non Hermitian fermion model containing a γ 5 matrix in the mass term m m 1 + γ 5 m 2 is con sidered. A new refined condition of the unbroken ᏼsymmetry of the theory is proposed that comprises an indication that the initial domain of unbroken ᏼsymmetry is divided into subdomains corresponding to the description of ordinary and exotic particles. A relationship is established between the theory under study and the quantum field theory with maximal mass M developed on the basis of the geometric approach. The operator Ꮿ is calculated explicitly, which is required for the construction of a new scalar product in the theory with a non Hermitian Hamiltonian.

On the basis of analytic solutions of Schrodinger and Pauli equations for a uniform magnetic field and a single attractive δ(r)-potential the equations for the bound oneactive electron states are discussed. It is vary important that ground electron states in the magnetic field essentially different from the analog state of spin-0 particles that binding energy has been intensively studied at more then forty years ago. We show that binding energy equations for spin-1/2 particles can be obtained without using of a well-known language of boundary conditions in the model of δ-potential that has been developed in pioneering works. Obtained equations are used for the analytically calculation of the energy level displacements, which demonstrate nonlinear dependencies on field intensities. It is shown that in a case of the weak intensity a magnetic field indeed plays a stabilizing role in considering systems. However the strong magnetic field shows the opposite action. We are expected that these properties can be of importance for real quantum mechanical fermionic systems in twoand three-dimensional cases. * Electronic address: vnrodionov@mtu-net.ru

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