 Majorana fermion operator

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:The canonical anticommutation relations verify their Hermiticity and normalization, and the occupation is $c^{†}c=(I+i{\gamma }_1{\gamma }_2)/2$.

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.