Triple

T5877440
Position Surface form Disambiguated ID Type / Status
Subject Schwinger–Dyson equations E130660 entity
Predicate relatedTo P37 FINISHED
Object Slavnov–Taylor identities
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.
E553294 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Slavnov–Taylor identities | Statement: [Schwinger–Dyson equations, relatedTo, Slavnov–Taylor identities]
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.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Slavnov–Taylor identities
Triple: [Schwinger–Dyson equations, relatedTo, Slavnov–Taylor identities]
Generated 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.
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

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69c0085523688190bfd487479ce819e6 completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c03630eefc8190ad1aaa1919ecf97f completed March 22, 2026, 6:34 p.m.
NED1 Entity disambiguation (via context triple) batch_69c0b12861c081909f95f1ef6a1f457c completed March 23, 2026, 3:19 a.m.
NEDg Description generation batch_69c0b299fe78819089a2ca8a1ae44329 completed March 23, 2026, 3:25 a.m.
NED2 Entity disambiguation (via description) batch_69c0b2ea7e60819099417b5acb21f8d0 completed March 23, 2026, 3:26 a.m.
Created at: March 22, 2026, 3:57 p.m.