We make a systematic investigation of all simple possibilities of having massive neutrinos in SU(2)×U(1) models of electroweak interactions, without the ad hoc imposition of lepton-number conservation. The minimal standard model is enlarged with triplet or singly or doubly charged singlet scalars as well as fermions in singlet and doublet representations. We find that in all cases the neutrino mass eigenstates are Majorana fields. This is so even though right-handed neutrino fields are added to the model. When mass terms of the Dirac type are also present (and if ${\nu }_R\text{'}\mathrm{s}$ also have small masses) neutrinos will oscillate into antineutrinos (which, we argue, are most likely "sterile"). General fermion mass terms of both Dirac and Majorana types are studied and the results are included in the Appendix.

• Received 27 June 1980

DOI:https://doi.org/10.1103/PhysRevD.22.2860