Two classes of Majorana neutrinos in the seesaw model

The commonly used pseudo-C symmetry (ν_L)^c=Cν_L‾^T is not defined in Lagrangian field theory. In general, there exist two classes of Majorana fermions: the first is associated with the Dirac-type fermion with the conventional C and P symmetries, and the second is associated with the Weyl-type fermion defined by CP symmetry only and formally characterized by the pseudo-C symmetry. Taking the seesaw model as an example, it is shown that a generalized Pauli–Gürsey (or Bogoliubov-type) canonical transformation converts the neutrino defined by the Weyl-type fermion to the neutrino defined by the Dirac-type fermion and thus to the conventional Majorana fermion, while preserving the canonical anti-commutation relations. The mixing angles in the weak lepton sector are not modified by this generalized Pauli–Gürsey transformation.