Galilei invariant wave equations (Q1973699)

The paper describes the quantum states of an elementary particle invariant with respect to a symmetry group as solutions of an invariant wave equation. The wave equation is defined as a family of differential operators acting on a space of vector-valued distributions over space-time. The space of the distributions carries a geometric representation of the symmetry group and the differential operators are invariant with respect to this action. For the Galilei invariant particles in 3+1 and 2+1 dimensions, the authors obtain interesting and nontrivial results.