On the Possibility of the Majorana Nature of Neutrino

The smallness of the neutrino mass is usually explained by the "seesaw" mechanism, in which the neutrino must be a Majorana fermion that coincides with its charge conjugate. Six nonequivalent concepts of charge conjugation are discussed in the literature, which correspond to six possible types of Majorana and Majorana-like fermions. These are charge conjugation according to Pauli; according to Majorana and Kramers; according to Schwinger; QFT conjugation according to Kramers; CP conjugation; CPTS conjugation according to Kayser and Goldhaber. We have proved that there can be only two variants of charge conjugation that would potentially allow the neutrino to be a Majorana-like fermion: unitary CP-conjugation and anti-unitary CPTS-conjugation proposed by Kayser and Goldhaber. We have obtained explicit formulas for these operators.