What is the influence of Hermitian condition ($\psi=\psi^{\dagger}$) of Majorana fermions operators in their statistical behavior?
A Majorana fermion gas must obey the Fermi-Dirac statistics, or their stastistical behavior may be anyonic?
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Sign up to join this communityWhat is the influence of Hermitian condition ($\psi=\psi^{\dagger}$) of Majorana fermions operators in their statistical behavior?
A Majorana fermion gas must obey the Fermi-Dirac statistics, or their stastistical behavior may be anyonic?
Majorana fermions as defined in http://en.wikipedia.org/wiki/Majorana_fermion are really fermions, as its name indicates. So Majorana fermion really have Fermi statistics. It is not proper to say Majorana fermions obey non-abelian statistics, since fermion always obey Fermi statistics by definition.
The thing that people said to have non-Abelian statistics are defects (such as vortices's) that carry a zero-energy mode. Such a thing is not Majorana fermions. Calling a zero mode as a Majorana fermion is really confusing.
Majorana fermions obey non-abelian statistics and it will be anyonic if your Majorana mode is confined to two dimensions. In $3\text{D}$, you still have the possibility of non-abelian statistics but it is no longer anyonic as the braid group is trivial.
Here are some useful references: