  It is demonstrated that the standard-model Lagrangian with a Majorana mass
term for the neutrino admits no non-trivial solution. Because the standard
model is generally believed to describe the gauge interactions of neutrinos
correctly, the Majorana mass term must vanish and thus cannot enable
neutrino-less double beta decay. More generally, neutrinos with standard-model
gauge interactions cannot be Majorana fields. Historical reasons why this
conclusion has not been drawn earlier are analyzed.
