Solution of the Majorana equation and its physical interpretation

Abstract This paper deals with the solution of the Majorana equation (ME) and its physical interpretation. A tutorial section on the standard Dirac equation presents the basic material required in the subsequent discussion of the ME. Its related purely imaginary gamma matrices and the associated generators of the Lorentz group are presented. Then, the solution of the real part of the ME is derived. Yet, the spinorial Lorentz transformation must also be considered and turns out to be the key for obtaining the complex spinor solution of the complete ME, in which the polarization matrix plays a prominent role. The associated complex spinor basis is derived, which encompasses the particle/antiparticle and spin-up/down duality. The symmetries of the Majorana equation are finally discussed together with the CPT theorem. In conclusion, the Majorana equation is fully equivalent to the usual Dirac equation. The physical consequences are discussed in the final section.