We start with reviewing the notion of continuous crossed products of von Neumann algebras by the action of some Abelian group. In this framework, Takesaki's duality is introduced. Restricting to the case when the Abelian group is R, allows us to make this consideration more “physical”. After that we discuss the relevance of this mathematical theory to physics. Towards this end, we briefly discuss two examples: Quantum Field Theory on de Sitter space (Witten et al) and the measurement problem in non-Abelian gauge theories (the work in progress with A. Balachandran).