View source for Poincaré group

The group of motions of [[Minkowski space|Minkowski space]]. The Poincaré group is the semi-direct product of the group of Lorentz transformations (cf. [[Lorentz transformation|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.



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

====References====
<table><TR><TD valign="top">[a1]</TD> <TD valign="top">  W. Rühl,   "The Lorentz group and harmonic analysis" , Benjamin  (1970)</TD></TR><TR><TD valign="top">[a2]</TD> <TD valign="top">  A.O. Barut,   R. Raçzka,   "Theory of group representations and applications" , '''1–2''' , PWN  (1977)  pp. Chapt. 17</TD></TR></table>