Physics:Quantum Fock space
Fock space is a Book I topic in the Quantum Collection. It is a Hilbert-space construction for quantum systems in which the number of particles is allowed to vary. The space is built from zero-particle, one-particle, two-particle, and higher-particle sectors, with symmetry imposed for bosons and antisymmetry for fermions. Creation and annihilation operators move states between these sectors. Fock space is central in quantum field theory, many-body physics, second quantization, photons, phonons, and the description of variable-particle-number processes.
Particle-number sectors
The zero-particle sector is the vacuum state. Applying a creation operator moves the system into a sector with one more excitation, while an annihilation operator lowers the particle number when possible.
For bosons, multiple particles can occupy the same mode. For fermions, occupation is restricted by antisymmetry and the Pauli exclusion principle. This makes Fock space useful for both radiation fields and electron systems.
Uses
In quantum optics, Fock states describe definite photon numbers. In condensed matter, the same formalism describes electrons, phonons, quasiparticles, and collective excitations.
Fock space is also the language behind perturbative field theory, scattering calculations, and many-particle Hamiltonians.
See also
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