There was a question about the difference between a neutrino and antineutrino, and answers suggested that weak isospin is different, as well as handedness. This would make sense if you expect pair production of neutrinos is possible, and weak isospin is conserved, you would expect equal and opposite values of weak isospin, but it is confusing when you consider that many theorists use the Majorana equation to describe neutrinos. The equation does not permit a distinction between particles and antiparticles in all reference frames. As far as I know, experimental scientists are still looking for violations of lepton number, so the Majorana neutrino could very well exist.
My question is if real neutrinos are Majorana neutrinos, does that mean their anti-particle does not have a different weak isospin from the particle. If the answer is they do have different weak isospin, are they really different particles.