Fermion with Three Mass Parameters

Abstract

In the chapter, starting from a 20-component wave function in general Gel’fand-Yaglom 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 nonvanishing 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.