  The Galilei group has been taken as the fundamental symmetry for
'nonrelativistic' physics, quantum or classical. Our fully group theoretical
formulation approach to the quantum theory asks for some adjustments. We
present a sketch of the full picture here, emphasizing aspects that are
different from the more familiar picture. The analysis involves a more careful
treatment of the relation between the exact mathematics and its physical
application in the dynamical theories, and a more serious full implementation
of the mathematical logic than what is usually available in the physics
literature. The article summarizes our earlier presented formulation while
focusing on the part beyond, with an adjusted, or corrected, identification of
the basic representations having the (Newtonian) mass as a Casimir invariant
and the notion of center of mass as dictated by the symmetry. Another result is
the necessary exclusion of the time translational symmetry, that otherwise bans
interactions between particles.
