Green's functions
E569215
Green's functions are mathematical tools used in physics and engineering to solve inhomogeneous differential equations and describe the propagation of fields or particles in space and time.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Green's functions canonical | 3 |
How this entity was disambiguated
This entity first appeared as the object of triple T6111228 — 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: Green's functions Context triple: [Peierls bracket, relatedTo, Green's functions]
-
A.
Wightman functions
Wightman functions are vacuum expectation values of time-ordered products of quantum fields that rigorously encode the correlation structure and axiomatic foundations of relativistic quantum field theory.
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B.
Born expansion of Green’s function
The Born expansion of Green’s function is a perturbative series representation used in scattering theory to express the Green’s function as a sum of successive interaction terms.
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C.
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.
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D.
Helmholtz equation
The Helmholtz equation is a fundamental partial differential equation that describes time-harmonic wave propagation in fields such as acoustics, electromagnetism, and optics.
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E.
Bessel functions
Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
- 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: Green's functions Target entity description: Green's functions are mathematical tools used in physics and engineering to solve inhomogeneous differential equations and describe the propagation of fields or particles in space and time.
-
A.
Wightman functions
Wightman functions are vacuum expectation values of time-ordered products of quantum fields that rigorously encode the correlation structure and axiomatic foundations of relativistic quantum field theory.
-
B.
Born expansion of Green’s function
The Born expansion of Green’s function is a perturbative series representation used in scattering theory to express the Green’s function as a sum of successive interaction terms.
-
C.
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.
-
D.
Helmholtz equation
The Helmholtz equation is a fundamental partial differential equation that describes time-harmonic wave propagation in fields such as acoustics, electromagnetism, and optics.
-
E.
Bessel functions
Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
- F. None of above. chosen
Statements (51)
| Predicate | Object |
|---|---|
| instanceOf |
integral kernel
ⓘ
mathematical concept ⓘ tool for solving differential equations ⓘ |
| alsoCalled | fundamental solution (in some contexts) ⓘ |
| definedBy | L G(x,x') = δ(x − x') for operator L ⓘ |
| dependsOn |
boundary conditions
ⓘ
geometry of the domain ⓘ |
| describes |
propagation of fields
ⓘ
propagation of particles ⓘ response to a point source ⓘ |
| hasType |
Euclidean Green's function
ⓘ
Feynman Green's function ⓘ advanced Green's function ⓘ causal Green's function ⓘ retarded Green's function ⓘ time-ordered Green's function ⓘ |
| historicalDevelopment | introduced in the 19th century by George Green ⓘ |
| namedAfter | George Green NERFINISHED ⓘ |
| property |
linearity with respect to the source term
ⓘ
symmetry under certain conditions (self-adjoint operators) ⓘ |
| relatedTo |
Dirac delta function
ⓘ
boundary integral methods ⓘ boundary value problems ⓘ convolution ⓘ initial value problems ⓘ linear differential operators ⓘ resolvent of an operator ⓘ spectral theory ⓘ |
| solves | inhomogeneous differential equations ⓘ |
| usedIn |
acoustics
ⓘ
applied mathematics ⓘ condensed matter physics ⓘ elasticity theory ⓘ electrodynamics ⓘ engineering ⓘ physics ⓘ potential theory ⓘ quantum field theory ⓘ quantum mechanics ⓘ signal processing ⓘ statistical mechanics ⓘ |
| usedToCompute |
Green's operators
ⓘ
propagators in quantum field theory ⓘ response functions ⓘ |
| usedToConstruct |
integral representations of solutions
ⓘ
solutions of linear inhomogeneous equations ⓘ |
| usedToSolve |
Helmholtz equation
NERFINISHED
ⓘ
Poisson's equation ⓘ Schrödinger equation (linear cases) NERFINISHED ⓘ diffusion equation ⓘ wave equation ⓘ |
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: Green's functions Description of subject: Green's functions are mathematical tools used in physics and engineering to solve inhomogeneous differential equations and describe the propagation of fields or particles in space and time.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
Partial Differential Equations