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The monograph is devoted to the construction of models of quantum physical systems on the basis of topology and functional analysis. Is introduced the hypothesis testing method in such quantum systems.more specifically in the book deals with a model of the global particle systems and their interaction, where the creation and annihilation operators represented as co boundary and boundary operators of the co chain and the chain complex of physical space (the space of pure state of the system) with coefficients in the presheaf and co-pre- sheaf of C algebra of observables. there also is constructed the deformation quantization method and model of gauge interactions where these interactions represent as generalization connectivity in a Gurevich`s fibering. With respect to the introduction of a method of testing the hypothesis in quantum systems, where for each system state constructed corresponding measure on the physical space and is built function of evaluation from space of samples (physical space) in the hypothesis space(space of system states)