Electric states and magnetic states in a Majorana field. (Part 1: electric states)

It is shown that the Mojarana condition, by which the Dirac equation is reduced to the so-called ''abbreviated'' equation, may be equivalently replaced in a gauge invariant way by the condition that the chiral invariant equals zero. This allows up to give a Lagrangian derivation of the Majorana field. Symmetry laws of this field, interacting with an electromagnetic field, are then investigated. The system is shown to be split (contrary to the Dirac field, but just as the monopole one) into two chiral components. The solution of the equation of such a chiral component is given in the case of a central electric field. It is shown that there are no bounds states but only ionized states which are a special superposition of positive and negative energy states. Finally the geometrical optics approximation is investigated and the Jacobi equation is solved for a chiral component in a central electric field. All the trajectories are hyperbolic but are not of the classical keplerian type. They are divided into two groups respectively corresponding to attractive and repulsive motions, whatever the particle charge may be