Abstract
We show that, contrary to the traditional assumption, the Majorana matrices define an algebra that is distinct from the algebra of the Dirac matrices. Furthermore, both algebras are in turn distinct from the Clifford algebra in Minkowski spacetime. This result is discussed within the context of field descriptions in four-dimensional spacetime. It is pointed out why these three algebras are almost impossible to distinguish in the representation space of 4 × 4 matrices.
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