When we speak of one particle in state ϕ ϕ i , we must bear in mind that in quantum mechanics identical particles are indistinguishable. In the same Fock space, all particles are identical. (To describe many species of particles, we take the tensor product of as many different Fock spaces as there are species of particles under consideration). It is one of the most powerful features of this formalism that states are implicitly properly symmetrized. For instance, if the above state | Ψ Ψ ⟩ ⟩ − − is fermionic, it will be 0 if two (or more) of the ϕ ϕ i are equal because the antisymmetric (exterior) product | ϕ ϕ i ⟩ ⟩ | ϕ ϕ i ⟩ ⟩ = 0 . This is a mathematical formulation of the Pauli exclusion principle that no two (or more) fermions can be in the same quantum state. In fact, whenever the terms in a formal product are linearly dependent; the product will be zero for antisymmetric tensors. Also, the product of orthonormal states is properly orthonormal by construction (although possibly 0 in the Fermi case when two states are equal).