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.
Aliases (3)
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
Lie group
→
mathematical group → non-abelian group → non-compact Lie group → symmetry group → |
| actsOn |
Minkowski spacetime
→
|
| category |
Lie groups
→
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
→
|
| 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
→
|
| hasRepresentationTheoryDevelopedBy |
Eugene Wigner
→
|
| hasSubgroup |
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 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 (7)
| Subject (surface form when different) | Predicate |
|---|---|
|
Lorentz group
→
Lorentz transformation → |
isSubgroupOf |
|
Poincaré group
("proper orthochronous Poincaré group")
→
|
hasConnectedComponent |
|
Poincaré group
("Poincaré algebra")
→
|
hasLieAlgebra |
|
Minkowski space-time
→
|
hasSymmetryGroup |
|
Henri Poincaré
→
|
notableWork |
|
Lorentz group
("Wigner classification")
→
|
usedIn |