Lorentz group

E32549

The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.

AI illustration

How this image was made

AI-generated illustration of Lorentz 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 Lorentz group (The Lorentz group is the mathematical group of spacetime symmetries in special relativity, consisting of all rotations and boosts that preserve the Minkowski spacetime interval.)

All labels observed (15)

How this entity was disambiguated

Statements (50)

Predicate Object
instanceOf Lie group ⓘ
mathematical group ⓘ
matrix group ⓘ
non-abelian group ⓘ
non-compact group ⓘ
real Lie group ⓘ
symmetry group ⓘ
actsOn Minkowski spacetime ⓘ
definedBy linear transformations preserving Minkowski bilinear form ⓘ
definedOn four-dimensional real vector space ⓘ
hasAlternativeName Lorentz transformations ⓘ
O(1,3) ⓘ
linked to: Lorentz group
hasApplicationIn general relativity (local tangent spaces) ⓘ
high-energy physics ⓘ
particle physics ⓘ
hasComponent connected component of identity ⓘ
four connected components ⓘ
hasCoveringGroup SL(2,C) ⓘ
hasDimension 6 ⓘ
hasGenerator boost generators ⓘ
rotation generators ⓘ
hasInvariant light cone structure ⓘ
spacetime interval ⓘ
hasLieAlgebra so(1,3) ⓘ
hasProperty non-compact simple Lie group up to discrete factors ⓘ
not simply connected ⓘ
hasRank 1 ⓘ
hasSignature (1,3) ⓘ
hasSubgroup boost subgroup ⓘ
orthochronous Lorentz group ⓘ
linked to: Lorentz group

proper Lorentz group ⓘ
linked to: Lorentz group

proper orthochronous Lorentz group SO^+(1,3) ⓘ
linked to: Lorentz group

rotation group SO(3) ⓘ
spatial rotation subgroup ⓘ
isIsomorphicTo SO^+(1,3) ⓘ
isLocallyIsomorphicTo SL(2,C) ⓘ
isSubgroupOf Poincaré group ⓘ
namedAfter Hendrik Lorentz ⓘ
preserves Minkowski metric ⓘ
Minkowski spacetime interval ⓘ
speed of light ⓘ
relatedTo Dirac equation ⓘ
relativistic quantum field theory ⓘ
representation theory ⓘ
special relativity ⓘ
spinors ⓘ
usedIn Wigner classification ⓘ
linked to: Poincaré group

classification of elementary particles ⓘ
formulation of relativistic invariance ⓘ
gauge theories ⓘ

How these facts were elicited

Referenced by (30)

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

Lorentz transformation → associatedWith → Lorentz group ⓘ
relativity of simultaneity → relatedTo → Lorentz invariance ⓘ
linked to: Lorentz group
Minkowski space-time → hasSubgroup → Lorentz group ⓘ
Hendrik Lorentz → knownFor → Lorentz invariance ⓘ
linked to: Lorentz group
Poincaré group → contains → Lorentz group ⓘ
Poincaré group → isSemidirectProductOf → Lorentz group ⓘ
Poincaré group → hasSubgroup → proper orthochronous Lorentz group ⓘ
linked to: Lorentz group
Lorentz group → hasSubgroup → proper Lorentz group ⓘ
linked to: Lorentz group
Lorentz group → hasSubgroup → orthochronous Lorentz group ⓘ
linked to: Lorentz group
Lorentz group → hasSubgroup → proper orthochronous Lorentz group SO^+(1,3) ⓘ
linked to: Lorentz group
Lorentz group → hasAlternativeName → O(1,3) ⓘ
linked to: Lorentz group
Lorentzian geometry → relatedTo → Lorentz group ⓘ
Hendrik Lorentz → notableFor → Lorentz invariance ⓘ
subject linked to: Lorentz
linked to: Lorentz group
Klein–Gordon equation → hasSymmetry → Lorentz invariance ⓘ
linked to: Lorentz group
Dirac matrices → associatedWith → Lorentz group ⓘ
AdS isometry group SO(2,d) → containsSubgroup → Lorentz group SO(1,d-1) ⓘ
linked to: Lorentz group
spin Casimir operator → hasProperty → Lorentz invariance ⓘ
linked to: Lorentz group
SL(2,C) → isDoubleCoverOf → SO^+(3,1) ⓘ
linked to: Lorentz group
SL(2,C) → isUniversalCoverOf → SO^+(3,1) ⓘ
linked to: Lorentz group
SL(2,C) → isSpinGroupFor → Lorentz group in 3+1 dimensions ⓘ
linked to: Lorentz group
SL(2,C) → isSpinGroupFor → SO(3,1) ⓘ
linked to: Lorentz group
SL(2,C) → quotientByCenterIsIsomorphicTo → SO^+(3,1) ⓘ
linked to: Lorentz group
Born–Infeld electrodynamics → hasProperty → Lorentz invariance ⓘ
linked to: Lorentz group
Invariance Principles and Elementary Particles → mainSubject → Lorentz invariance ⓘ
linked to: Lorentz group
Rindler coordinates → mathematicallyRelatedTo → Lorentz boosts ⓘ
linked to: Lorentz group
CPT theorem → isRelatedTo → Lorentz symmetry ⓘ
linked to: Lorentz group
Pauli–Lubanski pseudovector → relatedTo → Lorentz generators ⓘ
linked to: Lorentz group
Bondi–Metzner–Sachs symmetry → hasSubgroup → Lorentz subgroup ⓘ
linked to: Lorentz group
BMS group → containsSubgroup → Lorentz group ⓘ