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

Abstract

In a model of extended particles described by Minkowski space-time variables x, de Sitter internal variables ξ, a physical wave Ψx(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 Ψx (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.