Physics:Quantum Yang-Mills field - Revision history

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	A '''~~quantum~~ Yang-Mills field''' is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves.~~<ref>{{cite web \|title=~~Yang-Mills ~~theory \|url=https~~:~~//en.wikipedia~~.~~org/wiki/~~Yang~~%E2%80%93Mills_theory \|website=Wikipedia \|access~~-~~date=19 May 2026}}</ref><ref>{{cite book \|last1=Peskin \|first1=Michael E~~. ~~\|last2=Schroeder \|first2=Daniel V~~. ~~\|title=An Introduction to Quantum Field Theory \|publisher=Addison-Wesley \|year=1995 \|id=ISBN 978-0-201-50397-5}}</ref>~~		'''Yang-Mills field''' is a Book II topic in the Quantum Collection. A quantum Yang-Mills field is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves. A quantum Yang-Mills field is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves.
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	== Physical examples ==		== Physical examples ==
	Quantum chromodynamics is a Yang-Mills theory based on color SU(3), with gluon fields as its gauge fields. The electroweak theory also uses non-Abelian gauge fields before symmetry breaking separates the observed photon, W, and Z bosons.<ref>{{cite journal \|collaboration=Particle Data Group \|title=Review of Particle Physics \|journal=Physical Review D \|volume=110 \|issue=3 \|pages=030001 \|year=2024 \|id=DOI 10.1103/PhysRevD.110.030001}}</ref>		Quantum chromodynamics is a Yang-Mills theory based on color SU(3), with gluon fields as its gauge fields. The electroweak theory also uses non-Abelian gauge fields before symmetry breaking separates the observed photon, W, and Z bosons.<ref>{{cite journal \|collaboration=Particle Data Group \|title=Review of Particle Physics \|journal=Physical Review D \|volume=110 \|issue=3 \|pages=030001 \|year=2024 \|id=DOI 10.1103/PhysRevD.110.030001}}</ref>

			== Description ==
			'''Yang-Mills field''' is a matter-scale concept used to organize how quantum theory describes atoms, particles, fields, condensed matter, plasma, or spacetime-related systems. In the Quantum Collection it is placed by scale so the reader can move from materials and molecules down to subatomic degrees of freedom.

			== Quantum context ==
			At this scale, the relevant behavior is controlled by quantized states, interactions, conservation laws, and the way excitations or particles are observed. The concept is normally linked to measurable properties such as energy, momentum, charge, spin, spectra, scattering rates, or collective modes.

			== Role in the collection ==
			This page provides a compact reference point for related pages in Book II. It should be read together with nearby matter-scale topics and the corresponding foundations in [[Physics:Quantum mechanics\|quantum mechanics]].<ref name="matter-wiki">{{cite web \|url=https://en.wikipedia.org/wiki/Quantum_mechanics \|title=Quantum mechanics \|website=Wikipedia \|access-date=2026-05-20}}</ref>

	=See also=		=See also=

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	A '''quantum Yang-Mills field''' is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves.<ref>{{cite web \|title=Yang-Mills theory \|url=https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory \|website=Wikipedia \|access-date=19 May 2026}}</ref><ref>{{cite book \|last1=Peskin \|first1=Michael E. \|last2=Schroeder \|first2=Daniel V. \|title=An Introduction to Quantum Field Theory \|publisher=Addison-Wesley \|year=1995 \|~~isbn~~=978-0-201-50397-5}}</ref>		A '''quantum Yang-Mills field''' is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves.<ref>{{cite web \|title=Yang-Mills theory \|url=https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory \|website=Wikipedia \|access-date=19 May 2026}}</ref><ref>{{cite book \|last1=Peskin \|first1=Michael E. \|last2=Schroeder \|first2=Daniel V. \|title=An Introduction to Quantum Field Theory \|publisher=Addison-Wesley \|year=1995 \|id=ISBN 978-0-201-50397-5}}</ref>
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	== Gauge symmetry ==		== Gauge symmetry ==
	Yang-Mills theory begins with local gauge symmetry. The gauge field is introduced so that the theory remains consistent when internal symmetry transformations vary from point to point in spacetime.<ref>{{cite book \|last=Schwartz \|first=Matthew D. \|title=Quantum Field Theory and the Standard Model \|publisher=Cambridge University Press \|year=2014 \|~~isbn~~=978-1-107-03473-0}}</ref>		Yang-Mills theory begins with local gauge symmetry. The gauge field is introduced so that the theory remains consistent when internal symmetry transformations vary from point to point in spacetime.<ref>{{cite book \|last=Schwartz \|first=Matthew D. \|title=Quantum Field Theory and the Standard Model \|publisher=Cambridge University Press \|year=2014 \|id=ISBN 978-1-107-03473-0}}</ref>

	== Self-interaction ==		== Self-interaction ==
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	== Physical examples ==		== Physical examples ==
	Quantum chromodynamics is a Yang-Mills theory based on color SU(3), with gluon fields as its gauge fields. The electroweak theory also uses non-Abelian gauge fields before symmetry breaking separates the observed photon, W, and Z bosons.<ref>{{cite journal \|collaboration=Particle Data Group \|title=Review of Particle Physics \|journal=Physical Review D \|volume=110 \|issue=3 \|pages=030001 \|year=2024 \|~~doi~~=10.1103/PhysRevD.110.030001}}</ref>		Quantum chromodynamics is a Yang-Mills theory based on color SU(3), with gluon fields as its gauge fields. The electroweak theory also uses non-Abelian gauge fields before symmetry breaking separates the observed photon, W, and Z bosons.<ref>{{cite journal \|collaboration=Particle Data Group \|title=Review of Particle Physics \|journal=Physical Review D \|volume=110 \|issue=3 \|pages=030001 \|year=2024 \|id=DOI 10.1103/PhysRevD.110.030001}}</ref>

	=See also=		=See also=

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{{Short description|Non-Abelian gauge field used in modern field theory}}

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A '''quantum Yang-Mills field''' is a non-Abelian gauge field: a field associated with a symmetry group whose generators do not all commute. Yang-Mills fields generalize electromagnetism and are essential for the strong interaction, the weak interaction, and the structure of the Standard Model. Unlike the electromagnetic field, non-Abelian gauge fields can interact directly with themselves.<ref>{{cite web |title=Yang-Mills theory |url=https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory |website=Wikipedia |access-date=19 May 2026}}</ref><ref>{{cite book |last1=Peskin |first1=Michael E. |last2=Schroeder |first2=Daniel V. |title=An Introduction to Quantum Field Theory |publisher=Addison-Wesley |year=1995 |isbn=978-0-201-50397-5}}</ref>
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[[File:Quantum_Yang_Mills_field_yellow.png|thumb|280px|Yang-Mills field: non-Abelian gauge curvature and self-interacting field lines.]]
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== Gauge symmetry ==
Yang-Mills theory begins with local gauge symmetry. The gauge field is introduced so that the theory remains consistent when internal symmetry transformations vary from point to point in spacetime.<ref>{{cite book |last=Schwartz |first=Matthew D. |title=Quantum Field Theory and the Standard Model |publisher=Cambridge University Press |year=2014 |isbn=978-1-107-03473-0}}</ref>

== Self-interaction ==
Because the underlying symmetry is non-Abelian, the field strength contains terms in which gauge fields multiply one another. This produces self-interactions that are absent in ordinary Abelian electromagnetism.<ref>{{cite web |title=Yang-Mills theory |url=https://en.wikipedia.org/wiki/Yang%E2%80%93Mills_theory |website=Wikipedia |access-date=19 May 2026}}</ref>

== Physical examples ==
Quantum chromodynamics is a Yang-Mills theory based on color SU(3), with gluon fields as its gauge fields. The electroweak theory also uses non-Abelian gauge fields before symmetry breaking separates the observed photon, W, and Z bosons.<ref>{{cite journal |collaboration=Particle Data Group |title=Review of Particle Physics |journal=Physical Review D |volume=110 |issue=3 |pages=030001 |year=2024 |doi=10.1103/PhysRevD.110.030001}}</ref>

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

=References=
{{reflist|3}}

{{Author|Harold Foppele}}

{{Sourceattribution|Physics:Quantum Yang-Mills field|1}}