Fock Space

The Fock space is an algebraic construction used in quantum mechanics to construct the quantum states of a variable or unknown number of particles from a single particle Hilbert space . It is named after V. A. Fock who first introduced it in his paper Konfigurationsraum und zweite Quantelung.

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:

Here is the operator which symmetrizes or antisymmetrizes a tensor, depending on whether the Hilbert space describes particles obeying bosonic or fermionic statistics. The bosonic (resp. fermionic) Fock space can alternatively be constructed as (the Hilbert space completion of) the symmetric tensors (resp. alternating tensors ). For every basis for there is a natural basis of the Fock space, the Fock states.