Majorana fermion
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  creates a fermion in quantum state  (described by a real wave function), whereas the annihilation operator  annihilates it (or, equivalently, creates the corresponding antiparticle). For a Dirac fermion the operators  and  are distinct, whereas for a Majorana fermion they are identical. The ordinary fermionic annihilation and creation operators  and  can be written in terms of two Majorana operators  and  by