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Extensions of the Dyson mapping for products of any numbers of fermion and boson operators are suggested. Their general importance in obtaining the relationship between particle and subparticle quantum models and in particular between particle and subparticle nuclear models is discussed. An application in nuclear physics is demonstrated by introducing an interacting spinor model of the nucleus using a new type of supersymmetry, and by showing its ability to unify and derive dynamic symmetry nuclear models. Another application is demonstrated by suggesting a quark nuclear-plasma model and by showing that it is possible to give a foundation for such system models, including the transition from quark condensate into nucleons (nucleus) in one limit and quark chaotic behaviour (plasma) in another.

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