Lorentz group

E32549
Lie group mathematical group matrix group non-abelian group non-compact group real Lie group symmetry 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.

Jump to: Surface forms Statements Referenced by

Observed surface forms (6)

Surface form Occurrences
Lorentz invariance 2
O(1,3) 1
orthochronous Lorentz group 1

Statements (50)

Predicate Object
instanceOf Lie group ⓘ
mathematical group ⓘ
matrix group ⓘ
non-abelian group ⓘ
non-compact group ⓘ
real Lie group ⓘ
symmetry group ⓘ
actsOn Minkowski space-time ⓘ
surface form: Minkowski spacetime
definedBy linear transformations preserving Minkowski bilinear form ⓘ
definedOn four-dimensional real vector space ⓘ
hasAlternativeName Lorentz transformation ⓘ
surface form: Lorentz transformations

Lorentz group ⓘ
surface form: O(1,3)
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 ⓘ
Lorentz group self-linksurface differs ⓘ
surface form: orthochronous Lorentz group

Lorentz group self-linksurface differs ⓘ
surface form: proper Lorentz group

Lorentz group self-linksurface differs ⓘ
surface form: proper orthochronous Lorentz group SO^+(1,3)

rotation group SO(3) ⓘ
spatial rotation subgroup ⓘ
isIsomorphicTo SO^+(1,3) ⓘ
isLocallyIsomorphicTo SL(2,C) ⓘ
isSubgroupOf Poincaré group ⓘ
namedAfter Hendrik Lorentz ⓘ
preserves Minkowski space-time ⓘ
surface form: Minkowski metric

Minkowski spacetime interval ⓘ
speed of light ⓘ
relatedTo Dirac equation ⓘ
relativistic quantum field theory ⓘ
representation theory ⓘ
special relativity ⓘ
spinors ⓘ
usedIn Poincaré group ⓘ
surface form: Wigner classification

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

Referenced by (12)

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

Lorentz transformation → associatedWith → Lorentz group ⓘ
Poincaré group → contains → Lorentz group ⓘ
Lorentz group → hasAlternativeName → Lorentz group ⓘ
this entity surface form: O(1,3)
Lorentz group → hasSubgroup → Lorentz group self-linksurface differs ⓘ
this entity surface form: proper Lorentz group
Lorentz group → hasSubgroup → Lorentz group self-linksurface differs ⓘ
this entity surface form: orthochronous Lorentz group
Lorentz group → hasSubgroup → Lorentz group self-linksurface differs ⓘ
this entity surface form: proper orthochronous Lorentz group SO^+(1,3)
Minkowski space-time → hasSubgroup → Lorentz group ⓘ
Poincaré group → hasSubgroup → Lorentz group ⓘ
this entity surface form: proper orthochronous Lorentz group
Poincaré group → isSemidirectProductOf → Lorentz group ⓘ
Hendrik Lorentz → knownFor → Lorentz group ⓘ
this entity surface form: Lorentz invariance
Lorentzian geometry → relatedTo → Lorentz group ⓘ
relativity of simultaneity → relatedTo → Lorentz group ⓘ
this entity surface form: Lorentz invariance