Physics:Quantum Fock space - Revision history

Maintenance script: Use ScholarlyWiki page top template for concept page

2026-05-20T22:23:51Z

Use ScholarlyWiki page top template for concept page

← Older revision		Revision as of 22:23, 20 May 2026
Line 1:		Line 1:
	{{Short description\|Hilbert-space construction for variable particle number}}		{{Short description\|Hilbert-space construction for variable particle number}}
	{{Quantum book backlink\|Quantum field theory}}
			{{ScholarlyWiki page top
			\|backlink={{Quantum book backlink\|Quantum field theory}}
	{{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}}		{{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.]]
	[[File:Quantum_fock_space_yellow.png\|~~thumb\|right\|320px~~\|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>

	'''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]].
			}}

	== Particle-number sectors ==		== Particle-number sectors ==

Maintenance script: Simplify top image layout for Quantum concept page

2026-05-20T22:20:28Z

Simplify top image layout for Quantum concept page

← Older revision		Revision as of 22:20, 20 May 2026
Line 3:		Line 3:
	{{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}}		{{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}}

	~~<div style="display~~:~~flex; gap:24px; align-items:flex-start; max-width:1280px; clear:both;">~~		[[File:Quantum_fock_space_yellow.png\|thumb\|right\|320px\|Fock space as sectors with different particle numbers connected by creation and annihilation operators.]]
	~~<div style="flex:1 1 680px; min-width:0; line-height:1.55;">~~
	'''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 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]].
	~~</div>~~
	~~<div style="flex:0 0 380px; max-width:38%;">~~
	~~[[File:Quantum_fock_space_yellow.png\|thumb\|360px\|Fock space as sectors with different particle numbers connected by creation and annihilation operators.]]~~
	~~</div>~~
	~~</div>~~

	~~<div style="clear:both;"></div>~~

	== Particle-number sectors ==		== Particle-number sectors ==

Maintenance script: Improve top layout for Quantum concept page

2026-05-20T22:17:24Z

Improve top layout for Quantum concept page

← Older revision		Revision as of 22:17, 20 May 2026
Line 1:		Line 1:
	{{Short description\|Hilbert-space construction for variable particle number}}		{{Short description\|Hilbert-space construction for variable particle number}}
	{{Quantum book backlink\|Quantum field theory}}		{{Quantum book backlink\|Quantum field theory}}
	{{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}}		{{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}}

	~~[[File~~:~~Quantum_fock_space_yellow~~.~~png\|thumb\|280px\|Fock space as sectors with different particle numbers connected by creation and annihilation operators.]]~~		<div style="display:flex; gap:24px; align-items:flex-start; max-width:1280px; clear:both;">
			<div style="flex:1 1 680px; min-width:0; line-height:1.55;">
	'''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 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]].
			</div>
			<div style="flex:0 0 380px; max-width:38%;">
			[[File:Quantum_fock_space_yellow.png\|thumb\|360px\|Fock space as sectors with different particle numbers connected by creation and annihilation operators.]]
			</div>
			</div>

			<div style="clear:both;"></div>

	== Particle-number sectors ==		== Particle-number sectors ==

Maintenance script: Apply continuous Quantum previous-next navigation

2026-05-20T21:59:47Z

Apply continuous Quantum previous-next navigation

← Older revision		Revision as of 21:59, 20 May 2026
Line 1:		Line 1:
	{{Short description\|Hilbert-space construction for variable particle number}}		{{Short description\|Hilbert-space construction for variable particle number}}
	{{Quantum book backlink\|Quantum field theory}}		{{Quantum book backlink\|Quantum field theory}}
			{{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}}

	[[File:Quantum_fock_space_yellow.png\|thumb\|280px\|Fock space as sectors with different particle numbers connected by creation and annihilation operators.]]		[[File:Quantum_fock_space_yellow.png\|thumb\|280px\|Fock space as sectors with different particle numbers connected by creation and annihilation operators.]]

Maintenance script: Create Quantum Collection concept page

2026-05-20T21:55:53Z

Create Quantum Collection concept page

New page

{{Short description|Hilbert-space construction for variable particle number}}
{{Quantum book backlink|Quantum field theory}}

[[File:Quantum_fock_space_yellow.png|thumb|280px|Fock space as sectors with different particle numbers connected by creation and annihilation operators.]]

'''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]].

== 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 ==
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum Fock space|1}}