Reformulation of the Majorana Theory of the Neutrino

Abstract

The Majorana theory for a particle with mass is reformulated in terms of a two-component field. In this form it is seen that the theory goes over continuously to the Weyl-type two-component equation as the mass tends to zero. The asymmetries obtained in $\beta$ and $\mu$ decay experiments are shown to imply only that the neutrino mass is small—not that it is zero. Also the asymmetries are shown to be no more implied by the use of a two-component theory than by the use of a four-component one. Two-component theories do imply certain relations between mass, parity nonconservation, and double $\beta$ decay. That there are asymmetries is due to the fact that the interactions necessary to describe the physical world are not reflection-invariant.