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Complex vacuum fluctuation as a chaotic “limit” set of any Kleinian group transformation and the mass spectrum of high energy particle physics via spontaneous self-organization. (English) Zbl 1034.81514
Summary: First we give an introduction to the $$\mathcal E^{(\infty)}$$ quantum space-time theory from the point of view of nonlinear dynamics, complexity, string and KAM theory. Subsequently we give without proof several theorems that we consider to be fundamental to the foundation of any general theory for high energy particles interaction. The final picture seems to be a synthesis between compactified Kleinian groups acting on the essentially nonlinear dynamics of a KAM system, which enables us to give a very accurate estimation of the mass spectrum of the standard model, and further still we are granted a glimpse into the physics of grand unification as well as quantum gravity.

##### MSC:
 81R60 Noncommutative geometry in quantum theory 81V22 Unified quantum theories 37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics) 83C45 Quantization of the gravitational field 83E30 String and superstring theories in gravitational theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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