Abstract—An analysis is made of the possibility of generalizing Majorana’s theory based on the assumption
of the reality of this spinor field using the general principles of relativistic physics. An action functional is constructed for it that contains two parameters: one has the dimension of mass and the other is dimensionless.
Complete solutions of the Euler–Lagrange equations are found. An explicit form of the eigenspinors of the
helicity operator is obtained, which can be used as basic elements in describing the states of the system. In it,
in accordance with the results obtained by Majorana, the ordinary electric current is zero. The axial current
is nontrivial. Its main features are studied and, within the framework of the modification of Majorana’s theory, the possibility of participation of a real spinor fermionic field in electromagnetic interactions is discussed.