Schwinger–Dyson equations
E130660
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Dyson–Schwinger equations | 2 |
| Schwinger–Dyson equations canonical | 2 |
| Dyson equation | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1135190 — 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–Dyson equations Context triple: [Julian Schwinger, notableFor, Schwinger–Dyson equations]
-
A.
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.
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B.
Schwinger functions
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.
-
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.
Bethe–Salpeter equation
The Bethe–Salpeter equation is a relativistic quantum field theory equation that describes bound states of two interacting particles, such as electron–hole pairs in quantum electrodynamics.
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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–Dyson equations Target entity description: 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.
-
A.
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.
-
B.
Schwinger functions
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.
-
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.
Bethe–Salpeter equation
The Bethe–Salpeter equation is a relativistic quantum field theory equation that describes bound states of two interacting particles, such as electron–hole pairs in quantum electrodynamics.
-
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 (48)
| Predicate | Object |
|---|---|
| instanceOf |
equations of motion
ⓘ
integral equations ⓘ system of equations ⓘ |
| alsoKnownAs |
Schwinger–Dyson equations
ⓘ
surface form:
Dyson–Schwinger equations
|
| appliesTo |
gauge theories
ⓘ
interacting quantum field theories ⓘ non-perturbative quantum field theory ⓘ quantum chromodynamics ⓘ quantum electrodynamics ⓘ |
| assumes | existence of a well-defined path integral measure ⓘ |
| canBeWrittenAs | hierarchy of coupled integral equations ⓘ |
| centralConceptIn |
continuum functional methods
ⓘ
non-perturbative quantum field theory ⓘ |
| derivedFrom |
functional integral identity
ⓘ
invariance of the path integral under field shifts ⓘ path integral formalism ⓘ |
| encodes | full dynamics of a quantum field ⓘ |
| expressedInTermsOf |
effective action
ⓘ
generating functional of connected Green's functions ⓘ |
| field | quantum field theory ⓘ |
| forms | infinite tower of equations ⓘ |
| generalizes |
Heisenberg operator formulation of quantum mechanics
ⓘ
surface form:
Heisenberg equations of motion
classical Euler–Lagrange equations ⓘ |
| historicalDevelopment | formulated in mid-20th century ⓘ |
| mathematicalType |
functional differential equations
ⓘ
nonlinear integral equations ⓘ |
| namedAfter |
Freeman Dyson
ⓘ
Julian Schwinger ⓘ |
| relatedTo |
Bethe–Salpeter equation
ⓘ
Slavnov–Taylor identities ⓘ Ward–Takahashi identities ⓘ |
| relates |
Green's functions
ⓘ
n-point correlation functions ⓘ propagators ⓘ vertex functions ⓘ |
| requires |
renormalization for ultraviolet divergences
ⓘ
truncation schemes for practical calculations ⓘ |
| usedFor |
calculation of hadron properties
ⓘ
dynamical chiral symmetry breaking ⓘ non-perturbative studies of confinement ⓘ resummation of Feynman diagrams ⓘ study of fermion mass generation ⓘ study of gluon and ghost propagators ⓘ study of running coupling in QCD ⓘ |
| usedIn |
continuum QCD approaches
ⓘ
lattice gauge theory analyses ⓘ |
| validIn |
Euclidean space formulation
ⓘ
Minkowski space-time ⓘ
surface form:
Minkowski space formulation
|
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–Dyson equations Description of subject: 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.
Referenced by (5)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Dyson–Schwinger equations
this entity surface form:
Dyson–Schwinger equations
this entity surface form:
Dyson equation