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 (8)

Label	Occurrences
Yang–Mills theory canonical	6
Yang–Mills equations	3
Yang–Mills theories	2
N = 4 supersymmetric 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	Millennium Prize Problem ⓘ surface form: Clay 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 ⓘ surface form: Standard Model of particle physics electroweak theory ⓘ quantum chromodynamics ⓘ
generalizationOf	A Dynamical Theory of the Electromagnetic Field ⓘ surface form: Maxwell theory of electromagnetism
hasLagrangian	Yang–Mills theory self-linksurface differs ⓘ surface form: Yang–Mills Lagrangian
includesFeature	BRST symmetry ⓘ Faddeev–Popov ghosts ⓘ gauge fixing ⓘ nonlinear field equations ⓘ self-interaction of gauge bosons ⓘ
introducedBy	C. N. Yang ⓘ surface form: Chen-Ning 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	C. N. Yang ⓘ surface form: Chen-Ning 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	rotation group SU(2) ⓘ surface form: SU(2) SU(3) ⓘ special unitary group SU(n) ⓘ surface form: SU(N)

How these facts were elicited

Referenced by (16)

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 theory ⓘ

subject surface form: 't Hooft–Polyakov monopoles

this entity surface form: Yang–Mills–Higgs theories

’t Hooft–Polyakov monopoles → satisfy → Yang–Mills theory ⓘ

subject surface form: 't Hooft–Polyakov monopoles

this entity surface form: classical Yang–Mills equations

gluon → obeys → Yang–Mills theory ⓘ

this entity surface form: Yang–Mills equations

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 theory self-linksurface differs ⓘ

this entity surface form: Yang–Mills Lagrangian

Yang monopole → isSolutionOf → Yang–Mills theory ⓘ

this entity surface form: Yang–Mills equations

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

this entity surface form: Yang–Mills equations

Einstein–Yang–Mills equations → generalizes → Yang–Mills theory ⓘ

this entity surface form: flat-space Yang–Mills equations

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

this entity surface form: Yang–Mills theories

’t Hooft coupling → usedIn → Yang–Mills theory ⓘ

subject surface form: 't Hooft coupling

this entity surface form: N = 4 supersymmetric Yang–Mills theory

’t Hooft–Veltman gauge → appliesTo → Yang–Mills theory ⓘ

subject surface form: 't Hooft–Veltman gauge

this entity surface form: Yang–Mills theories

All labels observed (8)

How this entity was disambiguated Show

Statements (57)

How these facts were elicited Show

Referenced by (16)

How this entity was disambiguated

How these facts were elicited