Majorana spinor from the point of view of geometric algebra

Abstract

Majorana spinors are constructed in terms of the multivectors of relativistic Cl_1,3 algebra. Such spinors are found to be multiplied by primitive idempotents which drastically change spinor properties. Running electronic waves are used to solve the real Dirac–Majorana equation transformed to Cl_1,3 algebra. From the analysis of the solution it is concluded that free Majorana particles do not exist, because relativistic Cl_1,3 algebra requires the massive Majorana particle to move with light velocity.