Has it been done...? If so, any textbook on it...? The concept of Rigged Hilbert Spaces is essential to Quantum Mechanics. Symmetries are implemented in physics by doing representation theory of some symmetry groups, almost all of them being Lie groups: Galilei group, Poincaré group, Conformal group, SO(3), SU(n),... We actually know that what really is represented is the universal covering group for each group. So, since the natural setting for QM is a RHS, the continuous symmetries for a quantum theory need to be represented on this RHS... Daniel.