Yang–Mills theory

E244516

gauge theory non-abelian gauge theory quantum field theory theoretical physics concept

Yang–Mills theory is a gauge field theory describing the behavior of non-abelian gauge fields, forming the mathematical foundation for modern particle physics, including the strong and electroweak interactions.

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All labels observed (12)

Label	Occurrences
Yang–Mills theory canonical	14
Yang–Mills gauge theory	5
Yang–Mills equations	4
Yang–Mills instantons	3
Yang–Mills theories	3
N = 4 supersymmetric Yang–Mills theory	1
N=4 supersymmetric Yang–Mills theory	1
SU(2) Yang–Mills theory	1
Yang–Mills Lagrangian	1
Yang–Mills–Higgs theories	1
classical Yang–Mills equations	1
flat-space Yang–Mills equations	1

How this entity was disambiguated

This entity first appeared as the object of triple T2208686 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Yang–Mills theory
Context triple: [quantum chromodynamics, basedOn, Yang–Mills theory]

A. Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
B. Schwinger model
The Schwinger model is a two-dimensional quantum electrodynamics theory that serves as a exactly solvable toy model for studying phenomena like confinement, chiral symmetry breaking, and anomalies in quantum field theory.
C. Weyl’s gauge theory
Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
D. Yang–Mills existence and mass gap problem
The Yang–Mills existence and mass gap problem is a fundamental unsolved question in mathematical physics that asks for a rigorous proof that quantum Yang–Mills theory exists and exhibits a positive mass gap, and is one of the seven Millennium Prize Problems.
E. Schwinger–Dyson equations
The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Yang–Mills theory
Target entity description: Yang–Mills theory is a gauge field theory describing the behavior of non-abelian gauge fields, forming the mathematical foundation for modern particle physics, including the strong and electroweak interactions.

A. Chern–Simons theory
Chern–Simons theory is a topological quantum field theory in three dimensions that plays a central role in modern geometry, topology, and theoretical physics, particularly in the study of knot invariants and gauge fields.
B. Schwinger model
The Schwinger model is a two-dimensional quantum electrodynamics theory that serves as a exactly solvable toy model for studying phenomena like confinement, chiral symmetry breaking, and anomalies in quantum field theory.
C. Weyl’s gauge theory
Weyl’s gauge theory is an early 20th-century theoretical framework that introduced the concept of local gauge invariance, laying foundational ideas for modern gauge theories in particle physics.
D. Yang–Mills existence and mass gap problem
The Yang–Mills existence and mass gap problem is a fundamental unsolved question in mathematical physics that asks for a rigorous proof that quantum Yang–Mills theory exists and exhibits a positive mass gap, and is one of the seven Millennium Prize Problems.
E. Schwinger–Dyson equations
The Schwinger–Dyson equations are a set of integral equations in quantum field theory that relate correlation functions and encode the full dynamics of a quantum field.
F. None of above. chosen

Statements (57)

Predicate	Object
instanceOf	gauge theory ⓘ non-abelian gauge theory ⓘ quantum field theory ⓘ theoretical physics concept ⓘ
appliesToInteraction	electroweak interaction ⓘ strong interaction ⓘ weak interaction ⓘ
associatedPrize	Clay Millennium Prize Problem ⓘ linked to: Millennium Prize Problem
basedOn	Lie group symmetry ⓘ local gauge invariance ⓘ
classicalLimit	classical Yang–Mills equations ⓘ
coreConcept	covariant derivative ⓘ field strength tensor ⓘ gauge boson ⓘ gauge field ⓘ gauge invariance ⓘ non-abelian field strength ⓘ
describes	dynamics of gauge bosons ⓘ interactions mediated by gauge fields ⓘ non-abelian gauge fields ⓘ
field	mathematical physics ⓘ particle physics ⓘ theoretical physics ⓘ
foundationOf	Standard Model of particle physics ⓘ linked to: Standard Model electroweak theory ⓘ quantum chromodynamics ⓘ
generalizationOf	Maxwell theory of electromagnetism ⓘ linked to: A Dynamical Theory of the Electromagnetic Field
hasLagrangian	Yang–Mills Lagrangian ⓘ linked to: Yang–Mills theory
includesFeature	BRST symmetry ⓘ Faddeev–Popov ghosts ⓘ gauge fixing ⓘ nonlinear field equations ⓘ self-interaction of gauge bosons ⓘ
introducedBy	Chen-Ning Yang ⓘ linked to: C. N. Yang Robert Mills ⓘ
introducedInYear	1954 ⓘ
LagrangianTerm	−1/4 F^a_{μν} F^{a μν} ⓘ
mathematicalStructure	Lie algebra-valued gauge field ⓘ non-abelian field strength tensor ⓘ
namedAfter	Chen-Ning Yang ⓘ linked to: C. N. Yang Robert Mills ⓘ
openProblem	existence of a mass gap in 4D Yang–Mills theory ⓘ rigorous construction in four spacetime dimensions ⓘ
quantizedAs	quantum Yang–Mills theory ⓘ
relatedToConcept	Higgs mechanism ⓘ Wilson loop ⓘ asymptotic freedom ⓘ confinement ⓘ connection on a bundle ⓘ fiber bundle ⓘ mass gap ⓘ principal bundle ⓘ spontaneous symmetry breaking ⓘ
spacetimeDimension	typically 4 ⓘ
usesSymmetryGroup	SU(2) ⓘ linked to: rotation group SU(2) SU(3) ⓘ SU(N) ⓘ linked to: special unitary group SU(n)

How these facts were elicited

Referenced by (36)

Full triples — surface form annotated when it differs from this entity's canonical label.

quantum chromodynamics → basedOn → Yang–Mills theory ⓘ

C. N. Yang → knownFor → Yang–Mills theory ⓘ

Bianchi identities → usedIn → Yang–Mills theory ⓘ

Weyl’s gauge theory → inspiredConcept → Yang–Mills theory ⓘ

't Hooft–Polyakov monopoles → ariseIn → Yang–Mills–Higgs theories ⓘ

subject linked to: ’t Hooft–Polyakov monopoles

linked to: Yang–Mills theory

't Hooft–Polyakov monopoles → satisfy → classical Yang–Mills equations ⓘ

subject linked to: ’t Hooft–Polyakov monopoles

linked to: Yang–Mills theory

gluon → obeys → Yang–Mills equations ⓘ

linked to: Yang–Mills theory

Yang–Mills existence and mass gap problem → concerns → Yang–Mills theory ⓘ

Yang–Mills existence and mass gap problem → namedAfter → Yang–Mills theory ⓘ

Yang–Mills theory → hasLagrangian → Yang–Mills Lagrangian ⓘ

linked to: Yang–Mills theory

Yang monopole → isSolutionOf → Yang–Mills equations ⓘ

linked to: Yang–Mills theory

Einstein–Yang–Mills equations → basedOn → Yang–Mills equations ⓘ

linked to: Yang–Mills theory

Einstein–Yang–Mills equations → generalizes → flat-space Yang–Mills equations ⓘ

linked to: Yang–Mills theory

Kaluza–Klein theory → relatedTo → Yang–Mills theories ⓘ

linked to: Yang–Mills theory

't Hooft coupling → usedIn → N = 4 supersymmetric Yang–Mills theory ⓘ

subject linked to: ’t Hooft coupling

linked to: Yang–Mills theory

't Hooft–Veltman gauge → appliesTo → Yang–Mills theories ⓘ

subject linked to: ’t Hooft–Veltman gauge

linked to: Yang–Mills theory

Donaldson–Witten theory → relatedTo → Yang–Mills instantons ⓘ

linked to: Yang–Mills theory

Donaldson invariants → usesConcept → Yang–Mills theory ⓘ

Ward–Takahashi identities → appliesTo → Yang–Mills theories ⓘ

linked to: Yang–Mills theory

Slavnov–Taylor identities → usedIn → Yang–Mills theory ⓘ

Montonen–Olive duality → appliesTo → N=4 supersymmetric Yang–Mills theory ⓘ

linked to: Yang–Mills theory

Donaldson–Uhlenbeck–Yau theorem → relatedTo → Yang–Mills equations ⓘ

linked to: Yang–Mills theory

The Geometry of Four-Manifolds → mainSubject → Yang–Mills instantons ⓘ

subject linked to: The geometry of four-manifolds

linked to: Yang–Mills theory

The Geometry of Four-Manifolds → usesTool → Yang–Mills instantons ⓘ

subject linked to: The geometry of four-manifolds

linked to: Yang–Mills theory

Nielsen–Olesen instability → appliesTo → Yang–Mills theory ⓘ

Donaldson theory → uses → Yang–Mills gauge theory ⓘ

linked to: Yang–Mills theory

Robert Mills → notableWork → Yang–Mills theory ⓘ

Robert Mills → coDeveloperOf → Yang–Mills gauge theory ⓘ

linked to: Yang–Mills theory

Robert Mills → knownFor → Yang–Mills gauge theory ⓘ

linked to: Yang–Mills theory

Faddeev–Popov ghosts → usedIn → Yang–Mills theory ⓘ

Wilson loop → usedIn → Yang–Mills theory ⓘ

Seiberg–Witten invariants → relatedTo → Yang–Mills gauge theory ⓘ

linked to: Yang–Mills theory

Hodge star operator → importantIn → Yang–Mills theory ⓘ

Hitchin system → arisesFrom → Yang–Mills theory ⓘ

BPST instanton → theory → Yang–Mills gauge theory ⓘ

linked to: Yang–Mills theory

BPST instanton → theory → SU(2) Yang–Mills theory ⓘ

linked to: Yang–Mills theory

All labels observed (12)

How this entity was disambiguated Show

Statements (57)

How these facts were elicited Show

Referenced by (36)

How this entity was disambiguated

How these facts were elicited