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

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

The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.

Instruction

You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10.

# Requirements
- If you don't know the subject at all, return an empty list.
- If the subject is not a named entity, return an empty list.
- Include at least one triple where predicate is "instanceOf".
- Do not get too wordy.
- Separate several objects into multiple triples with one object.

Input

Subject: Yang–Mills theory
Description of subject: 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.

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