Poincaré group
E31560
The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
All labels observed (9)
How this entity was disambiguated
This entity first appeared as the object of triple T244269 — 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.
Target entity: Poincaré group Context triple: [Lorentz transformation, isSubgroupOf, Poincaré group]
-
A.
Minkowski space-time
Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
-
B.
Lorentz transformation
The Lorentz transformation is a set of equations in special relativity that relate space and time coordinates between two inertial reference frames moving at a constant velocity relative to each other, ensuring the constancy of the speed of light.
-
C.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
-
D.
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.
-
E.
de Sitter spacetime
de Sitter spacetime is a maximally symmetric, curved solution of general relativity that models an expanding universe dominated by a positive cosmological constant (dark energy).
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Target entity: Poincaré group Target entity description: The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
-
A.
Minkowski space-time
Minkowski space-time is a four-dimensional geometric framework that unifies three-dimensional space and time into a single continuum used to describe events and motion in special relativity.
-
B.
Lorentz transformation
The Lorentz transformation is a set of equations in special relativity that relate space and time coordinates between two inertial reference frames moving at a constant velocity relative to each other, ensuring the constancy of the speed of light.
-
C.
Noether's theorem
Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
-
D.
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.
-
E.
de Sitter spacetime
de Sitter spacetime is a maximally symmetric, curved solution of general relativity that models an expanding universe dominated by a positive cosmological constant (dark energy).
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
Lie group
ⓘ
mathematical group ⓘ non-abelian group ⓘ non-compact Lie group ⓘ symmetry group ⓘ |
| actsOn |
Minkowski space-time
ⓘ
surface form:
Minkowski spacetime
|
| category |
Lie group
ⓘ
surface form:
Lie groups
representation theory ⓘ theoretical physics ⓘ |
| contains |
Lorentz group
ⓘ
spacetime translations ⓘ |
| definedOn |
Minkowski space-time
ⓘ
surface form:
four-dimensional Minkowski space
|
| dimension | 10 ⓘ |
| generalizes | Euclidean group to Minkowski spacetime ⓘ |
| hasComponent |
boost transformations
ⓘ
space translations ⓘ spatial rotations ⓘ time translations ⓘ |
| hasConnectedComponent |
Poincaré group
self-linksurface differs
ⓘ
surface form:
proper orthochronous Poincaré group
|
| hasDiscreteSymmetryExtension |
parity transformation
ⓘ
space-time inversion ⓘ time reversal ⓘ |
| hasGenerator |
Hamiltonian (time translation generator)
ⓘ
angular momentum operators ⓘ boost generators ⓘ momentum operators ⓘ |
| hasInvariant |
Minkowski interval
ⓘ
mass Casimir operator ⓘ speed of light ⓘ spin Casimir operator ⓘ |
| hasLieAlgebra |
Poincaré group
self-linksurface differs
ⓘ
surface form:
Poincaré algebra
|
| hasRepresentationTheoryDevelopedBy | Eugene Wigner ⓘ |
| hasSubgroup |
Lorentz group
ⓘ
surface form:
proper orthochronous Lorentz group
rotation group SO(3) ⓘ three-dimensional spatial translation group ⓘ time translation group ⓘ |
| isExtensionOf | Galilean group (in relativistic regime) ⓘ |
| isSemidirectProductOf |
Lorentz group
ⓘ
translation group of Minkowski space ⓘ |
| isSymmetryOf |
Minkowski space-time
ⓘ
surface form:
Minkowski metric
free relativistic field theories ⓘ special relativity ⓘ vacuum of relativistic quantum field theory ⓘ |
| namedAfter | Henri Poincaré ⓘ |
| underlies |
classification of elementary particles
ⓘ
relativistic quantum field theory ⓘ |
| usedIn |
high-energy physics
ⓘ
particle physics ⓘ relativistic 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.
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.
Subject: Poincaré group Description of subject: The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
Referenced by (20)
Full triples — surface form annotated when it differs from this entity's canonical label.