 Pairing Majorana operators into a fermionic mode

Two distinct Majorana fermion operators with $\{{\gamma }_i,{\gamma }_j\}=2{\delta }_{ij}$ define the displayed fermionic annihilation operator. Direct multiplication gives $f^2=0$ and $\{f,f^{†}\}=1$. Its number operator is a projection operator with eigenvalues zero and one. An individual Hermitian Majorana operator has ${\gamma }_i^{†}{\gamma }_i={\gamma }_i^2=1$, so that expression is not a nontrivial occupation observable. The occupation belongs to a chosen pair. A quadratic coupling $iJ{\gamma }_a{\gamma }_b=J(2f^{†}f-1)$ splits the pair's two occupations by $2|J|$.