Fock space

The Fock space ( after the Russian physicist Vladimir Aleksandrovich Fock ) is used in quantum physics, especially in quantum field theory for the mathematical description of many-body systems with variable number of particles. Depending on whether they are bosons or fermions, the particles, one speaks of the bosonic or fermionic Fock space from. Its structure according to the Fock space is a quantum mechanical Hilbert space.

The basis states ( of a Fock space ) with a fixed number of particles ( that is, elements of density operators or above him, each of magnitude 1, or even the eigenstates of the particle number ) are called Fock states. One speaks in this context of second quantization or occupation number representation.

Mathematically

• The bosonic Fock space the symmetric tensor algebra or more precisely over a one-particle Hilbert space whose completion with respect to the scalar product
• The fermionic Fock space the Grassmann algebra over the one-particle Hilbert space, or more precisely their completion.

The appropriately normalized symmetrized tensor product ( in the bosonic case ) or the wedge product ( in the fermionic case ) induce pictures

With

The illustrations

Are called creation operators,

The adjoint operators to

Hot annihilation operators.

They apply to the canonical (anti) commutation relations

Where the upper sign ( commutator ) in the bosonic case and the lower sign ( anticommutator ) in the fermionic case applies.

• Quantum field theory
• Quantum mechanics