On solutions of the standard-model Lagrangian with a Majorana mass term

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.