Nonlinear Phenomena in Complex Systems, 2017, Vol.20, No.4, pp. 404

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2017, Vol.20, No.4, pp. 404 - 423

Spin 1/2 Particle with two Mass States: Interaction with External Fields
V. V. Kisel, V. A. Pletyukhov, V. V. Gilewsky, E. M. Ovsiyuk, O.V. Veko and V. M. Red’kov

In the paper, a model for spin 1/2 particle with two mass states is developed on the base of the Gel’fand–Yaglom approach in the theory of relativistic wave equations with extended sets of irreducible representations of the Lorentz group. The main generalized equation is presented in spin-tensor form, and with the use of the Dirac matrices. We introduce two auxiliary bispinors, they determine initial 16-component wave function, and in the absence of an external field for these bispinors we derive two separate Dirac-like equations with different masses M₁and M₂. It is shown that in the presence of external fields, electromagnetic field and gravitational non-Euclidean background with non-vanishing Ricci scalar curvature, the master wave equation is not split into separated equations, instead a quite definite mixing of two Dirac-like equations arises. This mixing also remains in the presence of only an electromagnetic field, as well it remains in the presence of only a gravitational field. It is shown that a generalized equation for Majorana particle with two mass parameters exists as well, such a generalized Majorana equation is not split into two separated equations if the Ricci scalar does not vanish.

Key words: Lorentz group, extended sets of representations, generalized wave equation, electromagnetic field, gravitational field, fermion with two masses parameters

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