Majorana neutrinos in seesaw mechanism and Bogoliubov quasiparticles

The idea that the Majorana neutrino should be identified as a Bogoliubov quasiparticle is applied to the seesaw mechanism for the three generations of neutrinos in the Standard Model. A relativistic analogue of the Bogoliubov transformation in the present context is a CP-preserving canonical transformation but modifies charge conjugation properties in such a way that the C-noninvariant fermion number violating term (condensate) is converted to a Dirac mass term. Puzzling aspects associated with the charge conjugation of chiral Weyl fermions are clarified. By invoking the Coleman--Weinberg mechanism in the framework of dimensional regularization, it is also noted that seesaw models become unnatural in some parameter regions which induce the hierarchy problems in the bosonic sector.