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 $\ensuremath{\beta}$ and $\ensuremath{\mu}$ 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 $\ensuremath{\beta}$ decay. That there are asymmetries is due to the fact that the interactions necessary to describe the physical world are not reflection-invariant.