Slavnov–Taylor identities
E553294
Slavnov–Taylor identities are relations in non-Abelian gauge theories that generalize Ward identities, ensuring the consistency and renormalizability of gauge-invariant quantum field theories.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Slavnov–Taylor identities canonical | 3 |
| Becchi–Rouet–Stora–Tyutin symmetry | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T5877440 — 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: Slavnov–Taylor identities Context triple: [Schwinger–Dyson equations, relatedTo, Slavnov–Taylor identities]
-
A.
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.
-
B.
Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
-
C.
Schrödinger functional equation in field theory
The Schrödinger functional equation in field theory is a generalization of the quantum-mechanical Schrödinger equation to quantum fields, describing the time evolution of wave functionals over field configurations.
-
D.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
E.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
- 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: Slavnov–Taylor identities Target entity description: Slavnov–Taylor identities are relations in non-Abelian gauge theories that generalize Ward identities, ensuring the consistency and renormalizability of gauge-invariant quantum field theories.
-
A.
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.
-
B.
Gell-Mann–Low theorem
The Gell-Mann–Low theorem is a fundamental result in quantum field theory that rigorously connects interacting quantum fields to free fields via the adiabatic switching-on of interactions, underpinning the use of perturbation theory and the Dyson series.
-
C.
Schrödinger functional equation in field theory
The Schrödinger functional equation in field theory is a generalization of the quantum-mechanical Schrödinger equation to quantum fields, describing the time evolution of wave functionals over field configurations.
-
D.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
E.
Tomonaga–Schwinger equation
The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
- F. None of above. chosen
Statements (44)
| Predicate | Object |
|---|---|
| instanceOf |
gauge theory identity
ⓘ
non-Abelian Ward identity ⓘ quantum field theory concept ⓘ |
| appliesTo | non-Abelian gauge theories ⓘ |
| assumes |
local gauge symmetry
ⓘ
renormalizable gauge theory ⓘ |
| category | symmetry identities in quantum field theory ⓘ |
| constrains |
propagators in gauge theories
ⓘ
renormalization constants of couplings ⓘ renormalization constants of fields ⓘ vertex functions ⓘ |
| dependsOn |
gauge-fixing terms
ⓘ
ghost fields ⓘ |
| derivedFrom |
BRST symmetry
ⓘ
gauge invariance of the path integral ⓘ |
| ensures |
consistency of gauge-invariant quantization
ⓘ
gauge invariance at the quantum level ⓘ renormalizability of gauge theories ⓘ |
| expressedIn |
configuration space
ⓘ
momentum space ⓘ |
| field |
gauge theory
ⓘ
quantum field theory ⓘ theoretical physics ⓘ |
| generalizes | Ward identities ⓘ |
| guarantees |
consistency of loop corrections with gauge invariance
ⓘ
preservation of gauge symmetry under renormalization ⓘ |
| holdsIn |
BRST-invariant quantization schemes
ⓘ
covariant gauges ⓘ |
| namedAfter |
Andrei Slavnov
ⓘ
John C. Taylor ⓘ |
| relatedTo |
Becchi–Rouet–Stora–Tyutin symmetry
ⓘ
linked to:
Slavnov–Taylor identities
Faddeev–Popov quantization ⓘ
linked to:
Faddeev–Popov ghosts
Ward–Takahashi identities ⓘ |
| relates |
Green’s functions in gauge theories
ⓘ
renormalization constants in gauge theories ⓘ |
| typeOf | functional identities ⓘ |
| usedFor |
checking gauge-parameter independence of observables
ⓘ
constraining counterterms ⓘ proving renormalizability of gauge theories ⓘ proving unitarity in gauge theories ⓘ |
| usedIn |
Yang–Mills theory
ⓘ
electroweak theory ⓘ
linked to:
Salam–Weinberg model
quantum chromodynamics ⓘ renormalization of non-Abelian gauge theories ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Slavnov–Taylor identities Description of subject: Slavnov–Taylor identities are relations in non-Abelian gauge theories that generalize Ward identities, ensuring the consistency and renormalizability of gauge-invariant quantum field theories.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Slavnov–Taylor identities