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.

All labels observed (11)

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 (24)

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