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If the Majorana fermion is a fermion that is it's own antiparticle and exactly the same as its fermion counterpart, then how do they know that it's not just a fermion?

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up vote 3 down vote accepted

A Majorana fermion would be a fermion that is it's own anti-particle. This is a common trait for bosons - the photon, gluon, and Z bosons are all their own anti-particles. Obviously, a Majorana fermion must not interact through the electromagnetic force, that is, it must have zero charge.

More technically, the wave equation that governs Majorana particles is a real wave equation. You can change a particle into its anti-particle by using complex conjugation (reversing the sign of complex numbers). Therefore, since it's a real wave equation, Majorana fermions would be their own anti-particles.

So, I think you are misunderstanding something - a Majorana fermion is a label applied to a fermion that is its own anti-particle. It's not that fermions have a Majorana fermion that they are related to, it's just a name for particles that are equivalent to their anti-particles.

For example, the neutrino may be a Majorana fermion. The way this can be tested is to see if double beta decay can occur without neutrinos. In double-beta decay, two neutrons in the nucleus are converted to protons, and two electrons and two electron antineutrinos are emitted. In neutrinoless double beta decay, the two neutrinos annihilate each other to produce two electrons, which is obviously only possible is the neutrino is a Majorana particle. This is a Feynman diagram of neutrinoless double beta decay.

Some more information on the Wiki page:

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Oh yes, it would seem that there was a misunderstanding there, as stated in paragraph 3. So, would a Majorana fermion not have an antiparticle counterpart then? e.g. if the electron was a Majorana fermion (which I know it isn't), there would be no antielectron/positron? Or am I getting confused? – Olly Price Aug 10 '12 at 19:33
Right, what we call an electron/positron pair would just be two electrons (or two positrons, since they would be the same thing!) – Mark M Aug 10 '12 at 19:40

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