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.

AI illustration

How this image was made

AI-generated illustration of Poincaré group

This AI-generated illustration was produced by black-forest-labs/FLUX.2-dev (1024x1024) from a prompt written by openai/gpt-oss-120b from the entity's label + description.

Prompt

Generate an image of the Poincaré group (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 (12)

How this entity was disambiguated

Statements (49)

Predicate Object
instanceOf Lie group ⓘ
mathematical group ⓘ
non-abelian group ⓘ
non-compact Lie group ⓘ
symmetry group ⓘ
actsOn Minkowski spacetime ⓘ
category Lie groups ⓘ
linked to: Lie group

representation theory ⓘ
theoretical physics ⓘ
contains Lorentz group ⓘ
spacetime translations ⓘ
definedOn four-dimensional Minkowski space ⓘ
dimension 10 ⓘ
generalizes Euclidean group to Minkowski spacetime ⓘ
hasComponent boost transformations ⓘ
space translations ⓘ
spatial rotations ⓘ
time translations ⓘ
hasConnectedComponent proper orthochronous Poincaré group ⓘ
linked to: 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 algebra ⓘ
linked to: Poincaré group
hasRepresentationTheoryDevelopedBy Eugene Wigner ⓘ
hasSubgroup proper orthochronous Lorentz group ⓘ
linked to: 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 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

Referenced by (30)

Full triples — surface form annotated when it differs from this entity's canonical label.

Lorentz transformation → isSubgroupOf → Poincaré group ⓘ
Minkowski space-time → hasSymmetryGroup → Poincaré group ⓘ
Henri Poincaré → notableWork → Poincaré group ⓘ
Poincaré group → hasLieAlgebra → Poincaré algebra ⓘ
linked to: Poincaré group
Poincaré group → hasConnectedComponent → proper orthochronous Poincaré group ⓘ
linked to: Poincaré group
Lorentz group → isSubgroupOf → Poincaré group ⓘ
Lorentz group → usedIn → Wigner classification ⓘ
linked to: Poincaré group
Euclidean group → relatedTo → Poincaré group ⓘ
AdS isometry group SO(2,d) → containsSubgroup → Poincaré group in d dimensions ⓘ
linked to: Poincaré group
Galilean group → contrastsWith → Poincaré group ⓘ
Galilean group → hasNonRelativisticLimitOf → Poincaré group ⓘ
Hamiltonian (time translation generator) → belongsTo → Poincaré symmetry algebra ⓘ
linked to: Poincaré group
Hamiltonian (time translation generator) → correspondsTo → time translation subgroup of Poincaré group ⓘ
linked to: Poincaré group
Minkowski interval → invariantUnder → Poincaré transformations ⓘ
linked to: Poincaré group
spin Casimir operator → associatedWith → Poincaré group ⓘ
spin Casimir operator → definedInTermsOf → Poincaré generators ⓘ
linked to: Poincaré group
spin Casimir operator → invariantUnder → Poincaré transformations ⓘ
linked to: Poincaré group
spin Casimir operator → relatedConcept → Poincaré algebra ⓘ
linked to: Poincaré group
Wightman axioms → usesConcept → Poincaré group ⓘ
Invariance Principles and Elementary Particles → mainSubject → Poincaré group ⓘ
Invariance Principles and Elementary Particles → usesConcept → Poincaré group ⓘ
Coleman–Mandula theorem → relatedTo → Poincaré group ⓘ
four-momentum operator → relatedTo → Poincaré group ⓘ
four-momentum operator → satisfies → Poincaré commutation relations ⓘ
linked to: Poincaré group
Pauli–Lubanski pseudovector → usedIn → Wigner classification ⓘ
linked to: Poincaré group
Pauli–Lubanski pseudovector → invariantUnder → Poincaré group translations ⓘ
linked to: Poincaré group
Bondi–Metzner–Sachs symmetry → extends → Poincaré symmetry ⓘ
linked to: Poincaré group
BMS group → containsSubgroup → Poincaré group ⓘ
BMS group → generalizes → Poincaré group ⓘ