Fock space

For a one-particle Hilbert space $H$, the bosonic or fermionic Fock space is ${\mathcal{F}}_{\pm }(H)={⨁}_{n=0}^{\infty }{H}^{{\otimes }_{\pm }n}$, using symmetric or antisymmetric tensor powers. Its zeroth summand is the one-dimensional vacuum sector. Creation operators and annihilation operators change particle number. The bosonic Fock space and fermionic Fock space implement the corresponding exchange statistics.

Fock space is a concept in quantum mechanics and quantum field theory that provides a framework for describing quantum states with a variable number of particles. It is particularly useful for systems where the number of particles is not fixed, such as in the contexts of particle physics, many-body systems, and condensed matter physics.