Quantum Theory as the Representation Theory of Symmetries

It is proposed that an unconstrained quantum system is completely specified by its configuration space $C$ and its group of symmetries $G$. It is then shown that the theory of projective unitary representations of $G$ on a certain Hilbert space determined by $C$ and $G$ leads to a definitive resolution of supposed ambiguities relating to superselection rules, choice of wave functions, topological properties of $G$ and $C$, anomalies, etc.