Physics:Quantum Fock space: Difference between revisions
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{{Short description|Hilbert-space construction for variable particle number}} | {{Short description|Hilbert-space construction for variable particle number}} | ||
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'''Quantum Fock space''' is a Hilbert-space construction used to describe systems with a variable number of particles. It is built as a direct sum of sectors containing zero particles, one particle, two particles, and so on.<ref>{{cite web |url=https://en.wikipedia.org/wiki/Fock_space |title=Fock space |publisher=Wikipedia |access-date=20 May 2026}}</ref> | {{Quantum article nav|previous=Physics:Quantum Second quantization|previous label=Second quantization|next=Physics:Quantum Harmonic Oscillator field modes|next label=Harmonic Oscillator field modes}} | ||
|image=[[File:Quantum_fock_space_yellow.png|430px|Fock space as sectors with different particle numbers connected by creation and annihilation operators.]] | |||
|text='''Quantum Fock space''' is a Hilbert-space construction used to describe systems with a variable number of particles. It is built as a direct sum of sectors containing zero particles, one particle, two particles, and so on.<ref>{{cite web |url=https://en.wikipedia.org/wiki/Fock_space |title=Fock space |publisher=Wikipedia |access-date=20 May 2026}}</ref> | |||
Fock space is central to [[Physics:Quantum field theory (QFT) basics|quantum field theory]], many-body physics, and quantum optics because particles can be created and destroyed. It provides the natural setting for [[Physics:Quantum Creation and annihilation operators|creation and annihilation operators]]. | Fock space is central to [[Physics:Quantum field theory (QFT) basics|quantum field theory]], many-body physics, and quantum optics because particles can be created and destroyed. It provides the natural setting for [[Physics:Quantum Creation and annihilation operators|creation and annihilation operators]]. | ||
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== Particle-number sectors == | == Particle-number sectors == | ||
Latest revision as of 22:23, 20 May 2026
Quantum Fock space is a Hilbert-space construction used to describe systems with a variable number of particles. It is built as a direct sum of sectors containing zero particles, one particle, two particles, and so on.[1]
Fock space is central to quantum field theory, many-body physics, and quantum optics because particles can be created and destroyed. It provides the natural setting for creation and annihilation operators.
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
- Physics:Quantum Creation and annihilation operators
- Physics:Quantum Second quantization
- Physics:Quantum many-body problem
- Physics:Quantum vacuum field
References
- ↑ "Fock space". Wikipedia. https://en.wikipedia.org/wiki/Fock_space.
Source attribution: Physics:Quantum Fock space