Un outil mathématique pour la physique : l'analyse non linéaire MinPlus et l' intégrale de chemin MinPlus

Abstract : In classical mechanics, there exists an analog to the Feynman path integral : the Minplus path integral that connects the Hamilton-Jacobi action S(x, t) to the Euler-Lagrange action S_cl (x, t; x0) by the equation : S(x, t) = min_x0 (S0(x0) + S_cl(x, t; x0)) (1) where the minimum is taken on the set of the initial positions x0 and where S0(x) is the Hamilton-Jacobi action at the initial time. This equation is an integral in the Minplus non-linear analysis [2] we introduced in 1996, following Maslov [1]. In classical mechanics, this equation explains the least action principle, and in quantum mechanics, it serves to refute Everett's many-worlds interpretation and strengthen the argument for the de Broglie-Bohm pilot wave for unbound particles (de Broglie-Bohm weak interpretation). In the conclusion, we discuss the wide-ranging potential this nonlinear analysis offers in physics.
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Michel Gondran, Alexandre Gondran. Un outil mathématique pour la physique : l'analyse non linéaire MinPlus et l' intégrale de chemin MinPlus. 19e Rencontre du Non Linéaire, Université Paris Diderot, Mar 2016, Paris, France. pp.31-36. ⟨hal-01348973v2⟩

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