On a generalization of canonical quantization

A study is made of Mackey's generalized quantization based on the concept of an imprimitivity system. Let $G$ be a topological group (symmetry group) acting continuously on a transitive $G$-space $X$ (the configuration space of a classical system). The structure of generalized imprimitivity systems is investigated in two cases: for a compact $G$ and for $G=X$ a locally compact type I group (for separable $G$ and Hilbert space $\mathscr H$ in which $G$ has a continuous unitary representation).
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