Poincaré group

From Encyclopedia of Mathematics
(Redirected from Poincare group)
Jump to: navigation, search

The group of motions of Minkowski space. The Poincaré group is the semi-direct product of the group of Lorentz transformations (cf. Lorentz transformation) and the group of four-dimensional displacements (translations). The Poincaré group is called after H. Poincaré, who first (1905) established that the Lorentz transformations form a group.


For a complete discussion of the representation theory of the Poincaré group cf. [a2]. The Poincaré group is also called the inhomogeneous Lorentz group.


[a1] W. Rühl, "The Lorentz group and harmonic analysis" , Benjamin (1970)
[a2] A.O. Barut, R. Raçzka, "Theory of group representations and applications" , 1–2 , PWN (1977) pp. Chapt. 17
How to Cite This Entry:
Poincare group. Encyclopedia of Mathematics. URL: