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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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[1] El Naschie, M.S., Superstrings, knots and non-commutative geometry in \(E\^{}\{(∞)\}\) space, Int. J. theor. phys., 37, 12, (1998) · Zbl 0935.58005
[2] El Naschie, M.S., Modular groups in Cantorian \(E\^{}\{(∞)\}\) high-energy physics, Chaos, solitons & fractals, 16, 353-366, (2003) · Zbl 1035.83503
[3] Marek-Crnjac, L., On mass spectrum of elementary particles of the standard model using el naschie’s Golden field theory, Chaos, solitons & fractals, 15, 611-618, (2003) · Zbl 1033.81521
[4] Ord, G., Classical particles and the Dirac equation with an electro-magnetic force, Chaos, solitons & fractals, 8, 5, 727-741, (1997) · Zbl 0940.81003
[5] Arnold, V.I., Geometrical methods in the theory of ordinary differential equations, (1983), Springer Verlag New York · Zbl 0507.34003
[6] Mumford D, Series C, Wright D. Indra’s Pearls. Cambridge, 2002 · Zbl 1141.00002
[7] El Naschie, M.S.; Rossler, O.; Prigogine, I., Quantum mechanics, diffusion and chaotic fractals, (1995), Elsevier Science-Pergamon Press Oxford · Zbl 0830.58001
[8] El Naschie, M.S., On the exact mass spectrum of quarks, Chaos, solitons & fractals, 14, 369-376, (2002)
[9] El Naschie, M.S.; Nottale, L.; Al Athel, S.; Ord, G., Fractal spacetime and Cantorian geometry in quantum mechanics, Chaos, solitons & fractals, 7, 6, (1996), [special issue]
[10] Beck, C., Spatio-temporal chaos and vacuum fluctuations of quantized fields, (2002), World Scientific Singapore · Zbl 1066.81621
[11] Kilmister CW. Eddington’s search for a fundamental theory. Cambridge, 1994
[12] ‘t Hooft G. In search of the ultimate building blocks. Cambridge, 1997 · Zbl 1344.81006
[13] El Naschie, M.S., Stress, stability and chaos, (1990), McGraw Hill London · Zbl 0729.73919
[14] Binnig G. Aus dem Nichts. Piper, Munich, 1989
[15] Guckenheim, J.; Holmes, P., Nonlinear oscillation, dynamical systems and bifurcation of vector fields, (1983), Springer New York
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