 Majorana mass term

A Majorana mass term pairs a Weyl spinor field with itself, schematically ${\mathcal{L}}_m=-\frac{1}{2}m\psi \psi +h.c.$ with the spinor indices contracted. Under the continuous phase rotation $\psi \mapsto e^{i\alpha }\psi$, the bilinear gains $e^{2i\alpha }$, so a nonzero fixed mass breaks that continuous number symmetry.

Gauge invariance requires the contracted bilinear to be a gauge singlet, not every component of the field to be a singlet. A suitable real representation, including the Adjoint representation, can admit an invariant Majorana mass term; an adjoint gaugino is an example. A single field with nonzero conserved electric charge cannot have such a term, because its pair carries twice that electric charge.^[ref]