ON GALILEI INVARIANCE IN QUANTUM-MECHANICS AND THE BARGMANN SUPERSELECTION RULE

We reinvestigate Bargmann's superselection rule for the overall mass o f n particles in ordinary quantum mechanics with Galilei invariant int eraction potential. We point out that in order for mass to define a su perselection rule it should be considered as a dynamical variable. We present a minimal extension of the original dynamics in which mass it treated as dynamical variable. Here the classical symmetry group turns out to be given by an R-extension of the Galilei group. Unlike before , there is now no obstruction to implement an action of the classical symmetry group on Hilbert space. We include some comments of a general nature on formal derivations of superselection rules without dynamica l context. (C) 1996 Academic Press, Inc.