he concept goes back to Majorana's 1937 suggestion[1] that neutral spin-1/2 particles can be described by a real wave equation (the Majorana equation), and would therefore be identical to their antiparticle (since the wave function of particle and antiparticle are related by complex conjugation).
The difference between Majorana fermions and Dirac fermions can be expressed mathematically in terms of the creation and annihilation operators of second quantization. The creation operator \gamma^{\dagger}_j creates a fermion in quantum state j (described by a real wave function), while the annihilation operator \gamma_j annihilates it (or, equivalently, creates the corresponding antiparticle). For a Dirac fermion the operators \gamma^{\dagger}_j and \gamma_j are distinct, while for a Majorana fermion they are identical.
Elementary particle[edit]
Since particles and antiparticles have opposite conserved charges, only an uncharged particle can have a Majorana mass[clarification needed]. All of the elementary fermions of the Standard Model have gauge charges, so they cannot have fundamental Majorana masses. However, the right-handed sterile neutrinos introduced to explain neutrino oscillation could have Majorana masses. If they do, then at low energy (after electroweak symmetry breaking), by the seesaw mechanism, the neutrino fields would naturally behave as six Majorana fields, with three expected to have very high masses (comparable to the GUT scale) and the other three expected to have very low masses (comparable to 1 eV). If right-handed neutrinos exist but do not have a Majorana mass, the neutrinos would instead behave as three Dirac fermions and their antiparticles with masses coming directly from the Higgs interaction, like the other Standard Model fermions.
The seesaw mechanism is appealing because it would naturally explain why the observed neutrino masses are so small. However, if the neutrinos are Majorana then they violate the conservation of
