On the role of some subgroups of the Poincaré group in models of high-energy physics.—I

Abstract

Inspired by the commonly known (2+1)-dimensional Galilei symmetry in the infinite-momentum frame, by the relation of the infinite-momentum limit to the contraction of the Poincare group, and by the possibility of rewriting the formulae of light front quantized theories in Galilei form, we decompose the representation spaces of the Poincare group into subspaces which are irreducible with respect to some (2+1)-dimensional Poincare subgroup of the Poincare group. After such a decomposition it is a simple corollary that (2+1)-dimensional Poincare symmetry is also possible in the infinite-momentum frame. It is shown in the example of the multiperipheral model that it can be of interest whether the Galilei or the Poincare subgroup is preferred.