Informally, a Fock space is the sum of a set of Hilbert spaces representing zero particle states, one particle states, two particle states, and so on. If the identical particles are bosons, the n -particle states are vectors in a symmetrized tensor product of n single-particle Hilbert spaces H. If the identical particles are fermions, the n -particle states are vectors in an antisymmetrized tensor product of n single-particle Hilbert spaces H (see symmetric algebra and exterior algebra respectively). A general state in Fock space is a linear combination of n -particle states, one for each n.