A second mistake: The second relation of the canonical (anti-)commutation relations, namely [a,a]=0, is not mentioned. For the single boson this is of no importance (since uv-uv=0). However, it is relevant for fermions since here one would get the constraint uv+uv=0 for a single fermionic mode which can only be satisfied by either u=0 or v=0. Consequence: One needs to consider at least two modes (e.g. spin up and down). Hence I would suggest to delete the paragraph about the single fermionic mode altogether and to extend the multi-mode section instead (referring to Bogoliubov-de Gennes Hamiltonians, see recent literature about topological insulators).