Poincaré group

E31560

Lie group mathematical group non-abelian group non-compact Lie group symmetry group

The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.

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All labels observed (9)

Label	Occurrences
Poincaré group canonical	10
Poincaré algebra	2
Poincaré transformations	2
Poincaré generators	1
Poincaré group in d dimensions	1
Poincaré symmetry algebra	1
Wigner classification	1
proper orthochronous Poincaré group	1
time translation subgroup of Poincaré group	1

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 ⓘ

Referenced by (20)

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 group self-linksurface differs ⓘ

this entity surface form: Poincaré algebra

Poincaré group → hasConnectedComponent → Poincaré group self-linksurface differs ⓘ

this entity surface form: proper orthochronous Poincaré group

Lorentz group → isSubgroupOf → Poincaré group ⓘ

Lorentz group → usedIn → Poincaré group ⓘ

this entity surface form: Wigner classification

Euclidean group → relatedTo → Poincaré group ⓘ

AdS isometry group SO(2,d) → containsSubgroup → Poincaré group ⓘ

this entity surface form: Poincaré group in d dimensions

Galilean group → contrastsWith → Poincaré group ⓘ

Galilean group → hasNonRelativisticLimitOf → Poincaré group ⓘ

Hamiltonian (time translation generator) → belongsTo → Poincaré group ⓘ

this entity surface form: Poincaré symmetry algebra

Hamiltonian (time translation generator) → correspondsTo → Poincaré group ⓘ

this entity surface form: time translation subgroup of Poincaré group

Minkowski interval → invariantUnder → Poincaré group ⓘ

this entity surface form: Poincaré transformations

spin Casimir operator → associatedWith → Poincaré group ⓘ

spin Casimir operator → definedInTermsOf → Poincaré group ⓘ

this entity surface form: Poincaré generators

spin Casimir operator → invariantUnder → Poincaré group ⓘ

this entity surface form: Poincaré transformations

spin Casimir operator → relatedConcept → Poincaré group ⓘ

this entity surface form: Poincaré algebra

Wightman axioms → usesConcept → Poincaré group ⓘ

Minkowski metric η_{μν} → invarianceGroup → Poincaré group ⓘ