Physics:Quantum gauge theory - Revision history

WikiHarold: Clean Quantum page image and red links

2026-05-23T23:34:28Z

Clean Quantum page image and red links

← Older revision		Revision as of 23:34, 23 May 2026
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	<div style="width:300px;">		<div style="width:300px;">
	[[File:~~File not found~~.~~png~~\|thumb\|280px\|~~No image available~~.]]		[[File:Quantum_gauge_theory_concept_map.svg\|thumb\|280px\|gauge theory in the Quantum Collection.]]
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	===Gauge fixing===		===Gauge fixing===

	In quantum physics, in order to ~~[[Physics:Quantization\|~~quantize]] a ~~[[Physics:Gauge theory\|~~gauge theory]], for example the [[Yang–Mills theory]], ~~[[Physics:Chern–Simons theory\|~~Chern–Simons theory]] or the ~~[[Physics:BF model\|~~BF model]], one method is to perform ~~[[Physics:Gauge fixing\|~~gauge fixing]]. This is done in the BRST and Batalin-Vilkovisky formulation.		In quantum physics, in order to quantize a gauge theory, for example the Yang–Mills theory, Chern–Simons theory or the BF model, one method is to perform gauge fixing. This is done in the BRST and Batalin-Vilkovisky formulation.

	===Wilson loops===		===Wilson loops===

	Another method is to factor out the symmetry by dispensing with ~~[[Physics:Vector potential\|~~vector ~~potential]]s~~ altogether (since they are not physically ~~[[Physics:Observable\|~~observable]]) and by working directly with ~~[[Physics:~~Wilson ~~loop\|Wilson loop]]s~~, Wilson lines contracted with other charged fields at its endpoints and ~~[[Physics:Spin network\|~~spin ~~network]]s~~.		Another method is to factor out the symmetry by dispensing with vector potentials altogether (since they are not physically observable) and by working directly with Wilson loops, Wilson lines contracted with other charged fields at its endpoints and spin networks.

	===Lattices===		===Lattices===

	An alternative approach using lattice approximations is covered in (Wick rotated) ~~[[Physics:Lattice gauge theory\|~~lattice gauge theory]].		An alternative approach using lattice approximations is covered in (Wick rotated) lattice gauge theory.

	===Older approaches===		===Older approaches===

	Older approaches to quantization for [[Abelian ~~group\|Abelian]]~~ models use the Gupta-Bleuler formalism with a "~~[[Semi-Hilbert space\|~~semi-Hilbert space]]" with an indefinite ~~[[Sesquilinear form\|~~sesquilinear form]]. However, it is much more elegant{{clarify\|date=May 2016}} to work with the ~~[[Quotient space (topology)\|~~quotient space]] of vector field configurations by gauge transformations.		Older approaches to quantization for Abelian models use the Gupta-Bleuler formalism with a "semi-Hilbert space" with an indefinite sesquilinear form. However, it is much more elegant{{clarify\|date=May 2016}} to work with the quotient space of vector field configurations by gauge transformations.

	== Quantum Yang–Mills theory ==		== Quantum Yang–Mills theory ==

	To establish the existence of the Yang-Mills theory and a ~~[[Physics:Mass gap\|~~mass gap]] is one of the seven Millennium Prize Problems of the Clay Mathematics Institute.		To establish the existence of the Yang-Mills theory and a mass gap is one of the seven Millennium Prize Problems of the Clay Mathematics Institute.

	A positive estimate from below of the mass gap in the spectrum of quantum Yang-Mills Hamiltonian has been already established.<ref>{{cite journal \|last=Dynin \|first=A. \|date=January 2017 \|title=Mathematical quantum Yang-Mills theory revisited \|journal=Russian Journal of Mathematical Physics \|volume=24 \|issue=1 \|pages=26–43\|bibcode=2017RJMP...24...19D \|arxiv=1308.6571 \|doi=10.1134/S1061920817010022 }}</ref>		A positive estimate from below of the mass gap in the spectrum of quantum Yang-Mills Hamiltonian has been already established.<ref>{{cite journal \|last=Dynin \|first=A. \|date=January 2017 \|title=Mathematical quantum Yang-Mills theory revisited \|journal=Russian Journal of Mathematical Physics \|volume=24 \|issue=1 \|pages=26–43\|bibcode=2017RJMP...24...19D \|arxiv=1308.6571 \|doi=10.1134/S1061920817010022 }}</ref>
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	==References==		==References==
	{{reflist}}		{{reflist}}

	~~{{Quantum field theories}}~~

	[[Category:Quantum field theory]]		[[Category:Quantum field theory]]

	{{Sourceattribution\|Quantum gauge theory\|1}}		{{Sourceattribution\|Quantum gauge theory\|1}}

WikiHarold: Expand short Quantum intro

2026-05-23T22:58:40Z

Expand short Quantum intro

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	~~{{hatnote\|See [[Physics:~~Gauge ~~theory\|~~gauge theory]] for the ~~classical preliminaries~~.}}		Quantum gauge theory is a Book I topic in the Quantum Collection. It studies quantum field theories whose interactions are organized by local symmetry transformations. Gauge symmetry introduces fields that mediate forces, such as the electromagnetic field in quantum electrodynamics and the gluon field in quantum chromodynamics. Quantizing a gauge theory requires special care because not all field components represent physical degrees of freedom. Gauge fixing, BRST symmetry, path integrals, Wilson loops, and lattice methods are tools for handling this structure. The topic links symmetry, conservation laws, particles, fields, and the mathematical foundations of modern fundamental physics.
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	[[Category:Quantum field theory]]		[[Category:Quantum field theory]]



	{{Sourceattribution\|Quantum gauge theory\|1}}		{{Sourceattribution\|Quantum gauge theory\|1}}

Harold: Add missing image fallback to Quantum header

2026-05-17T22:33:12Z

Add missing image fallback to Quantum header

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	~~<!--~~ No ~~lead~~ image available ~~in existing page~~. ~~-->~~		[[File:File not found.png\|thumb\|280px\|No image available.]]
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Harold: Restore Quantum article header template

2026-05-17T21:52:34Z

Restore Quantum article header template

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			{{Short description\|Quantum physics topic}}

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

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	{{hatnote\|See [[Physics:Gauge theory\|gauge theory]] for the classical preliminaries.}}		{{hatnote\|See [[Physics:Gauge theory\|gauge theory]] for the classical preliminaries.}}
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	==Quantization==		==Quantization==

imported>WikiHarold: simplify

2022-10-23T08:04:54Z

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imported>WikiHarold: simplify

2022-10-23T08:04:54Z

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New page

{{hatnote|See [[Physics:Gauge theory|gauge theory]] for the classical preliminaries.}}
==Quantization==

===Gauge fixing===

In quantum physics, in order to [[Physics:Quantization|quantize]] a [[Physics:Gauge theory|gauge theory]], for example the [[Yang–Mills theory]], [[Physics:Chern–Simons theory|Chern–Simons theory]] or the [[Physics:BF model|BF model]], one method is to perform [[Physics:Gauge fixing|gauge fixing]]. This is done in the BRST and Batalin-Vilkovisky formulation.

===Wilson loops===

Another method is to factor out the symmetry by dispensing with [[Physics:Vector potential|vector potential]]s altogether (since they are not physically [[Physics:Observable|observable]]) and by working directly with [[Physics:Wilson loop|Wilson loop]]s, Wilson lines contracted with other charged fields at its endpoints and [[Physics:Spin network|spin network]]s.

===Lattices===

An alternative approach using lattice approximations is covered in (Wick rotated) [[Physics:Lattice gauge theory|lattice gauge theory]].

===Older approaches===

Older approaches to quantization for [[Abelian group|Abelian]] models use the Gupta-Bleuler formalism with a "[[Semi-Hilbert space|semi-Hilbert space]]" with an indefinite [[Sesquilinear form|sesquilinear form]]. However, it is much more elegant{{clarify|date=May 2016}} to work with the [[Quotient space (topology)|quotient space]] of vector field configurations by gauge transformations.

== Quantum Yang–Mills theory ==

To establish the existence of the Yang-Mills theory and a [[Physics:Mass gap|mass gap]] is one of the seven Millennium Prize Problems of the Clay Mathematics Institute.

A positive estimate from below of the mass gap in the spectrum of quantum Yang-Mills Hamiltonian has been already established.<ref>{{cite journal |last=Dynin |first=A. |date=January 2017 |title=Mathematical quantum Yang-Mills theory revisited |journal=Russian Journal of Mathematical Physics |volume=24 |issue=1 |pages=26–43|bibcode=2017RJMP...24...19D |arxiv=1308.6571 |doi=10.1134/S1061920817010022 }}</ref>

==References==
{{reflist}}

{{Quantum field theories}}

[[Category:Quantum field theory]]

{{Sourceattribution|Quantum gauge theory|1}}