An extended Galilei group and its application

Abstract

The Galilei group is combined with two one-dimensional groups, to form a twelve-dimensional extended Galilei group. Irreducible representations of this group depend upon two indicesm, s that can, respectively, be interpreted as the mass and spin of a non-relativistic particle. It turns out that the true irreducible representations of the ordinary Galilei group correspond tom=0, and this explains why these representations have no physical interpretation.