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Functional Realization and Nonlinear Induced Representation in the Geometrodifferential Conception of Extended Particles

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Abstract

In a model of extended particles described by Minkowski space-time variables x, de Sitter internal variables ξ, a physical wave Ψ x (ξ) representing the proper characteristics of the particles, and a functional wave X [ Ψ ] giving previsions, we study functional propagation of X in the space of physical waves (as advocated by a quantum functional theory) as well as the nonlinear realization of the internal de Sitter group on its Lorentz subgroup (introduced by Drechsler). The first study is undertaken in a special instance Ψ x (ξ) = ξ(x), while in the second the general structure of the model is adopted and curved space-time treated, but the functional propagation is not considered. A fiber bundle structure and an induced representation method are used. Propagators are derived, a quantum version of a variant of Drechsler's theory is obtained, and a nonlinear version of our model is constructed.

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Hachemane, M., Smida, A. & Djelid, R. Functional Realization and Nonlinear Induced Representation in the Geometrodifferential Conception of Extended Particles. Foundations of Physics 29, 1479–1495 (1999). https://doi.org/10.1023/A:1018817411585

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  • DOI: https://doi.org/10.1023/A:1018817411585

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