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V.V. Kisel^{1}, V.A. Pletyukhov^{2}, E.M. Ovsiyuk^{3}, Ya.A. Voynova^{4}, V.M. Redkov^{4}

^{1} Belarus State University of Informatics and Radio-electronics, Belarus

^{2} Brest State University, Belarus

^{3 }Mozyr State Pedagogical University, Belarus

^{4} Institute of Physics, National Academy of Sciences of Belarus, Belarus

**Part of the book: **Future Relativity, Gravitation, Cosmology

In the chapter, starting from a 20-component wave function in general Gel’fandYaglom approach a new wave equation for spin 1/2 fermion, which is characterized by three mass parameters, is derived. In absence of external field, three involved bispinors obey three separate Dirac-like equations with different masses M1, M2, M3. In presence of external electromagnetic fields or non-Euclidean background with non-vanishing Ricci scalar curvature, the main equation is not split into separated equations, instead a quite definite mixing of three Dirac-like equations arises. It is shown that a generalized equation for Majorana particle with three mass parameters exists as well, such a generalized Majorana equation is not split into three separated equations in curved space-time if the Ricci scalar of the space-time model does not vanish.

**Keywords:** Lorentz group, extended sets of representations, generalized wave equation,

fermion, mass parameters, electromagnetic field, gravitational field.

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