Yang–Mills theory
E244516
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.
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 |
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 ⓘ |
| 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
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.
subject linked to:
’t Hooft–Polyakov monopoles
linked to: Yang–Mills theory
subject linked to:
’t Hooft–Polyakov monopoles
linked to: Yang–Mills theory
linked to: Yang–Mills theory
linked to: Yang–Mills theory
linked to: Yang–Mills theory
linked to: Yang–Mills theory
linked to: Yang–Mills theory
subject linked to:
’t Hooft coupling
linked to: Yang–Mills theory
subject linked to:
’t Hooft–Veltman gauge
linked to: Yang–Mills theory