Technically, the Fock space is (the Hilbert space completion of) the direct sum of the symmetric or antisymmetric tensors in the tensor powers of a single-particle Hilbert space H, F ν ν ( H ) = ⨁ ⨁ n = 0 ∞ ∞ S ν ν H ⊗ ⊗ n ¯ ¯ .