Schwinger functions
E59637
Schwinger functions are Euclidean-space correlation functions in quantum field theory that encode the theory’s dynamics and can be analytically continued to yield physical Minkowski-space Green’s functions.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Schwinger functions canonical | 5 |
| Minkowski-space Green’s functions | 1 |
| Schwinger functionals | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T478498 — 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: Schwinger functions Context triple: [Euclidean quantum field theory, hasKeyConcept, Schwinger functions]
-
A.
Euclidean quantum field theory
Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
-
B.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
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C.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
-
D.
Feynman path integral
The Feynman path integral is a formulation of quantum mechanics in which a particle’s behavior is described as a sum over all possible paths it can take, each weighted by a phase factor derived from the classical action.
-
E.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
- 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: Schwinger functions Target entity description: Schwinger functions are Euclidean-space correlation functions in quantum field theory that encode the theory’s dynamics and can be analytically continued to yield physical Minkowski-space Green’s functions.
-
A.
Euclidean quantum field theory
Euclidean quantum field theory is a formulation of quantum field theory in imaginary (Euclidean) time that enables rigorous mathematical treatment and path-integral representations closely connected to statistical mechanics.
-
B.
Faddeev’s axioms
Faddeev’s axioms are a set of conditions characterizing Shannon entropy in information theory, providing an alternative but equivalent axiomatization to the Shannon–Khinchin framework.
-
C.
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED
Dyson’s proof of equivalence of Feynman and Schwinger–Tomonaga formulations of QED is a landmark theoretical result that rigorously demonstrated the mathematical consistency and mutual compatibility of different approaches to quantum electrodynamics.
-
D.
Feynman path integral
The Feynman path integral is a formulation of quantum mechanics in which a particle’s behavior is described as a sum over all possible paths it can take, each weighted by a phase factor derived from the classical action.
-
E.
Feynman diagrams
Feynman diagrams are graphical representations used in quantum field theory to visualize and calculate particle interactions and processes.
- F. None of above. chosen
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
Euclidean correlation function
ⓘ
Green’s function in Euclidean space ⓘ object in quantum field theory ⓘ |
| analogousTo | correlation functions in classical statistical mechanics ⓘ |
| associatedWith |
Euclidean action
ⓘ
partition function of a quantum field theory ⓘ |
| canBeAnalyticallyContinuedTo |
Wightman correlation functions
ⓘ
time-ordered Green’s functions ⓘ |
| canBeObtainedBy | Wick rotating Minkowski correlation functions ⓘ |
| definedAs | vacuum expectation values of products of fields in Euclidean space ⓘ |
| dependsOn |
Euclidean time variables
ⓘ
spatial coordinates ⓘ |
| domain | n-fold Cartesian product of Euclidean space ⓘ |
| encode | dynamics of a quantum field theory ⓘ |
| field | quantum field theory ⓘ |
| framework |
axiomatic quantum field theory
ⓘ
constructive quantum field theory ⓘ |
| historicalContext | introduced in the development of Euclidean quantum field theory ⓘ |
| involves |
Euclidean metric
ⓘ
imaginary time formalism ⓘ |
| mathematicalNature |
generalized functions
ⓘ
tempered distributions ⓘ |
| namedAfter | Julian Schwinger ⓘ |
| order | n-point correlation function ⓘ |
| relatedConcept |
generating functional
ⓘ
propagator ⓘ two-point function ⓘ |
| relatedTo |
Euclidean quantum field theory
ⓘ
Schwinger functions self-linksurface differs ⓘ
surface form:
Minkowski-space Green’s functions
Osterwalder–Schrader axioms ⓘ
surface form:
Osterwalder–Schrader reconstruction theorem
Euclidean quantum field theory ⓘ
surface form:
Wick rotation
Wightman functions ⓘ analytic continuation ⓘ path integral formulation ⓘ |
| satisfies |
Euclidean invariance
ⓘ
Osterwalder–Schrader axioms ⓘ cluster decomposition property ⓘ reflection positivity ⓘ symmetry under permutations of arguments ⓘ |
| spaceTimeDomain | Euclidean space ⓘ |
| usedFor |
defining Euclidean functional integrals
ⓘ
lattice gauge theory calculations ⓘ non-perturbative studies of quantum field theories ⓘ reconstructing Minkowski-space quantum field theories ⓘ |
| usedIn |
lattice QCD
ⓘ
Euclidean quantum field theory ⓘ
surface form:
statistical field theory
|
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: Schwinger functions Description of subject: Schwinger functions are Euclidean-space correlation functions in quantum field theory that encode the theory’s dynamics and can be analytically continued to yield physical Minkowski-space Green’s functions.
Referenced by (7)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Schwinger functionals
this entity surface form:
Minkowski-space Green’s functions