Physics:Quantum Second quantization - Revision history

Harold: /* See also */

2026-05-23T22:43:31Z

See also

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	One is not quantizing "again", as the term "second" might suggest; the field that is being quantized is not a Schrödinger wave function that was produced as the result of quantizing a particle, but is a classical field (such as the electromagnetic field or Dirac spinor field), essentially an assembly of coupled oscillators, that was not previously quantized. One is merely quantizing each oscillator in this assembly, shifting from a semiclassical treatment of the system to a fully quantum-mechanical one.		One is not quantizing "again", as the term "second" might suggest; the field that is being quantized is not a Schrödinger wave function that was produced as the result of quantizing a particle, but is a classical field (such as the electromagnetic field or Dirac spinor field), essentially an assembly of coupled oscillators, that was not previously quantized. One is merely quantizing each oscillator in this assembly, shifting from a semiclassical treatment of the system to a fully quantum-mechanical one.

	~~== See also ==~~
	=See also=		=See also=
	{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}		{{#invoke:PhysicsQC\|tocHeadingAndList\|Physics:Quantum basics/See also}}

2026-05-22T11:33:24Z

Normalize quantum page header order

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	{{Quantum book backlink\|Quantum field theory}}		{{Quantum book backlink\|Quantum field theory}}
	{{Quantum article nav\|previous=Physics:Quantum Fields and Particles\|previous label=Fields and Particles\|next=Physics:Quantum Fock space\|next label=Fock space}}		{{Quantum article nav\|previous=Physics:Quantum Fields and Particles\|previous label=Fields and Particles\|next=Physics:Quantum Fock space\|next label=Fock space}}

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2026-05-22T11:11:43Z

Clean Book label remnants and backlink spacing

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	{{Short description\|Formulation of the quantum many-body problem}}		{{Short description\|Formulation of the quantum many-body problem}}

	{{Quantum book backlink\|Quantum field theory}}		{{Quantum book backlink\|Quantum field theory}}
	{{Quantum article nav\|previous=Physics:Quantum Fields and Particles\|previous label=Fields and Particles\|next=Physics:Quantum Fock space\|next label=Fock space}}		{{Quantum article nav\|previous=Physics:Quantum Fields and Particles\|previous label=Fields and Particles\|next=Physics:Quantum Fock space\|next label=Fock space}}

2026-05-22T11:03:56Z

Remove hidden BOM characters and direct Book label after Short description

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	{{Short description\|Formulation of the quantum many-body problem}}~~Book I~~		{{Short description\|Formulation of the quantum many-body problem}}

	{{Quantum book backlink\|Quantum field theory}}		{{Quantum book backlink\|Quantum field theory}}

2026-05-22T10:48:59Z

Clean Short description prefix and add Book I label

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	~~~~{{Short description\|Formulation of the quantum many-body problem}}		{{Short description\|Formulation of the quantum many-body problem}}Book I

	{{Quantum book backlink\|Quantum field theory}}		{{Quantum book backlink\|Quantum field theory}}

2026-05-20T21:59:45Z

Apply continuous Quantum previous-next navigation

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	{{Short description\|Formulation of the quantum many-body problem}}		{{Short description\|Formulation of the quantum many-body problem}}

	{{Quantum book backlink\|Quantum field theory}}		{{Quantum book backlink\|Quantum field theory}}
	{{Quantum article nav\|previous=Physics:Quantum Fields and Particles\|previous label=Fields and Particles\|next=Physics:Quantum ~~Harmonic Oscillator field modes~~\|next label=~~Harmonic Oscillator field modes~~}}		{{Quantum article nav\|previous=Physics:Quantum Fields and Particles\|previous label=Fields and Particles\|next=Physics:Quantum Fock space\|next label=Fock space}}

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2026-05-20T12:25:58Z

Apply Quantum previous-next navigation

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	{{Short description\|Formulation of the quantum many-body problem}}		{{Short description\|Formulation of the quantum many-body problem}}

	{{Quantum book backlink\|Quantum field theory}}		{{Quantum book backlink\|Quantum field theory}}
			{{Quantum article nav\|previous=Physics:Quantum Fields and Particles\|previous label=Fields and Particles\|next=Physics:Quantum Harmonic Oscillator field modes\|next label=Harmonic Oscillator field modes}}

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2026-05-20T08:16:19Z

Clean Book I red links, intro, and image slots

2026-05-19T22:50:20Z

Normalize Book I Quantum page structure

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	[[Category:Mathematical quantization]]		[[Category:Mathematical quantization]]

	{{Sourceattribution\|Quantum Second quantization\|1}}		{{Sourceattribution\|Physics:Quantum Second quantization\|1}}

2026-05-17T14:02:03Z

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 {{Quantum book backlink|Quantum field theory}}
 '''Second quantization''', also referred to as '''occupation number representation''', is a formalism used to describe and analyze [[Physics:Quantum mechanics|quantum]] [[Physics:N-body problem|many-body]] systems. In [[Physics:Quantum field theory|quantum field theory]], it is known as [[Physics:Canonical quantization|canonical quantization]], in which the fields (typically as the wave functions of matter) are thought of as [[Physics:Field operator|field operator]]s, in a manner similar to how the physical quantities (position, momentum, etc.) are thought of as operators in [[Physics:First quantization|first quantization]]. The key ideas of this method were introduced in 1927 by [[Biography:Paul Dirac|Paul Dirac]],<ref name="Dirac1927">{{cite journal
   | last = Dirac
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   | doi-access = free
   }}</ref> The second quantization formalism introduces the [[Physics:Creation and annihilation operators|creation and annihilation operators]] to construct and handle the Fock states, providing useful tools to the study of the quantum many-body theory.
 {{Quantum field theory}}
 == Quantum many-body states ==