For fermions, the commutator is replaced by the anticommutator { ⋅ ⋅ , ⋅ ⋅ } , { a i , a j † † } ≡ ≡ a i a j † † + a j † † a i = δ δ i j , { a i † † , a j † † } = { a i , a j } = 0. Therefore, exchanging disjoint (i.e. i ≠ ≠ j ) operators in a product of creation or annihilation operators will reverse the sign in fermion systems, but not in boson systems.