= Majorana fermion operator
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{wiki}
A Majorana fermion operator is a <self-adjoint operator> in a fermionic algebra satisfying $\{\gamma_i,\gamma_j\}=2\delta_{ij}I$. A single complex fermionic mode $c$ can be written using two such operators:
$$
\gamma_1=c+c^\dagger,\qquad \gamma_2=-i(c-c^\dagger),\qquad c=\frac{\gamma_1+i\gamma_2}{2}.
$$
The <canonical anticommutation relations> verify their Hermiticity and normalization, and the occupation is $c^\dagger c=(I+i\gamma_1\gamma_2)/2$.
This algebraic rewriting is always possible for a complex mode. A spatially separated <Majorana zero mode> requires additional physical properties, including localization and near-zero commutator with the <Hamiltonian>. The existence of two Majorana operators in a formula alone therefore does not establish protected boundary states or a topological phase.
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