It appears that all fundamental particles in nature that are spin-1/2 are described by the Dirac equation, with the possible exception of the neutrino. There does not seem to be any a priori reason why this would be the case. A perfectly valid choice for spinors would be the non-complexified version of Cℓ 2,2 ( R ), the Majorana spinor. There also does not seem to be any particular prohibition to having Weyl spinors appear in nature as fundamental particles.