Klein–Gordon equation
E118070
The Klein–Gordon equation is a relativistic wave equation that describes spin-0 (scalar) particles in quantum field theory.
All labels observed (6)
| Label | Occurrences |
|---|---|
| Klein–Gordon equation canonical | 11 |
| Klein-Gordon equation | 1 |
| Klein-Gordon operator | 1 |
| Klein–Gordon equation scattering | 1 |
| Klein–Gordon equations | 1 |
| Klein–Gordon–Fock equation | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T1006214 — 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: Klein–Gordon equation Context triple: [Dirac equation, generalizes, Klein–Gordon equation]
-
A.
Dirac equation
The Dirac equation is a fundamental relativistic wave equation in quantum mechanics that describes spin-½ particles such as electrons and predicts phenomena like antimatter.
-
B.
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.
-
C.
Einstein–Maxwell equations
The Einstein–Maxwell equations are the coupled set of field equations in general relativity that describe how spacetime curvature and electromagnetic fields interact and influence each other.
-
D.
Lorentz
Lorentz is a Dutch surname most famously associated with physicist Hendrik Lorentz, a pioneer of electromagnetic theory and relativity.
-
E.
Maxwell's equations
Maxwell's equations are the fundamental set of four equations in classical electromagnetism that describe how electric and magnetic fields are generated and interact with charges and currents.
- 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: Klein–Gordon equation Target entity description: The Klein–Gordon equation is a relativistic wave equation that describes spin-0 (scalar) particles in quantum field theory.
-
A.
Dirac equation
The Dirac equation is a fundamental relativistic wave equation in quantum mechanics that describes spin-½ particles such as electrons and predicts phenomena like antimatter.
-
B.
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.
-
C.
Einstein–Maxwell equations
The Einstein–Maxwell equations are the coupled set of field equations in general relativity that describe how spacetime curvature and electromagnetic fields interact and influence each other.
-
D.
Lorentz
Lorentz is a Dutch surname most famously associated with physicist Hendrik Lorentz, a pioneer of electromagnetic theory and relativity.
-
E.
Maxwell's equations
Maxwell's equations are the fundamental set of four equations in classical electromagnetism that describe how electric and magnetic fields are generated and interact with charges and currents.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
field equation
ⓘ
partial differential equation ⓘ relativistic wave equation ⓘ |
| appliesTo |
bosons
ⓘ
charged scalar fields ⓘ neutral scalar fields ⓘ pseudoscalar mesons ⓘ |
| assumes | special relativity ⓘ |
| couplesTo | electromagnetic field via minimal coupling ⓘ |
| covariantDerivativeSymbol | D_μ ⓘ |
| definedOn |
Minkowski spacetime
ⓘ
linked to:
Minkowski space-time
|
| derivedFrom | relativistic energy–momentum relation ⓘ |
| describes |
scalar particles
ⓘ
spin-0 particles ⓘ |
| fieldType | scalar field ⓘ |
| generalizes | classical wave equation ⓘ |
| hasConservedQuantity |
charge
ⓘ
four-current ⓘ |
| hasDispersionRelation | ω^2 = k^2 + m^2 ⓘ |
| hasForm |
(∂_μ ∂^μ + m^2) φ(x) = 0
ⓘ
(□ + m^2) φ = 0 ⓘ |
| hasIssue | non-positive-definite probability density in single-particle interpretation ⓘ |
| hasKineticTerm | ∂_μ φ ∂^μ φ ⓘ |
| hasLagrangianDensity | ℒ = 1/2 (∂_μ φ ∂^μ φ − m^2 φ^2) ⓘ |
| hasMassTerm | m^2 φ ⓘ |
| hasNo | spinor indices ⓘ |
| hasOperator | dAlembert operator ⓘ |
| hasOrder |
second order in space
ⓘ
second order in time ⓘ |
| hasSolutionType | plane waves ⓘ |
| hasSpinDescription | spin-0 ⓘ |
| hasSymmetry |
Lorentz invariance
ⓘ
linked to:
Lorentz group
|
| hasVariant | massless Klein–Gordon equation ⓘ |
| masslessForm | □ φ = 0 ⓘ |
| minimalCouplingForm | (D_μ D^μ + m^2) φ = 0 ⓘ |
| namedAfter |
Oskar Klein
ⓘ
Walter Gordon ⓘ |
| obtainedFrom | Euler–Lagrange equation ⓘ |
| precedes | Dirac equation ⓘ |
| relatedTo |
E^2 = p^2 + m^2
ⓘ
Proca equation ⓘ Schrödinger equation in nonrelativistic limit ⓘ |
| resolvedBy | quantum field theoretic interpretation ⓘ |
| symbolUses |
m
ⓘ
φ(x) ⓘ ∂_μ ⓘ |
| usedIn |
quantum field theory
ⓘ
relativistic quantum mechanics ⓘ |
| yearIntroduced | 1926 ⓘ |
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: Klein–Gordon equation Description of subject: The Klein–Gordon equation is a relativistic wave equation that describes spin-0 (scalar) particles in quantum field theory.
Referenced by (16)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Klein–Gordon equation
subject linked to:
"Advanced Quantum Mechanics"
linked to: Klein–Gordon equation
linked to: Klein–Gordon equation
linked to: Klein–Gordon equation
linked to: Klein–Gordon equation