Abstract
In a Majorana basis, the Dirac equation for a free spin one-half particle is a 4x4 real matrix differential equation. The solution can be a Majorana spinor, a 4x1 real column matrix, whose entries are real functions of the space-time. Can a Majorana spinor, whose entries are real functions of the space-time, describe the energy, linear and angular momentums of a free spin one-half particle? We show that it can. We show that the Majorana spinor is an irreducible representation of the double cover of the proper orthochronous Lorentz group and of the full Lorentz group. The Fourier-Majorana and Hankel-Majorana transforms are defined and related to the linear and angular momentums of a free spin one-half particle.
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