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Average exceptional Lie and Coxeter group hierarchies with special reference to the standard model of high energy particle physics

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  • El Naschie, M.S.

Abstract

The notions of the order of a symmetry group may be extended to that of an average, non-integer order. Building on this extension, it can be shown that the five classical exceptional Lie symmetry groups could be extended to a hierarchy, the total sum of which is four times α¯0=137+k0 of the electromagnetic field. Subsequently it can be shown that all known and conjectured physical fields may be derived by E-infinity transfinite scaling transformation. Consequently E8E8 exceptional Lie symmetry groups manifold, the SL(2,7)c holographic modular curve boundary Γ(7), Einstein–Kaluza gravity R(n=4) and R(n=5) as well as the electromagnetic field are all topological transformations of each other. It is largely a matter of mathematical taste to choose E8 or the electromagnetic field associated with α¯0 as derived or as fundamental. However since E8 has been extensively studied by the founding father of group theory and has recently been mapped completely, it seems beneficial to discuss at least high energy physics starting from the largest of the exceptional groups.

Suggested Citation

  • El Naschie, M.S., 2008. "Average exceptional Lie and Coxeter group hierarchies with special reference to the standard model of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 662-668.
  • Handle: RePEc:eee:chsofr:v:37:y:2008:i:3:p:662-668
    DOI: 10.1016/j.chaos.2008.01.018
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    References listed on IDEAS

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    1. El Naschie, M.S., 2008. "High energy physics and the standard model from the exceptional Lie groups," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 1-17.
    2. El Naschie, M.S., 2008. "Conjectures regarding kissing spheres hierarchy and quantum gravity unification," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 346-350.
    3. He, Ji-Huan & Xu, Lan & Zhang, Li-Na & Wu, Xu-Hong, 2007. "Twenty-six dimensional polytope and high energy spacetime physics," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 5-13.
    4. El Naschie, M.S., 2008. "Quarks confinement via Kaluza–Klein theory as a topological property of quantum classical spacetime phase transition," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 825-829.
    5. Marek-Crnjac, L., 2007. "Fuzzy Kähler manifolds," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 677-681.
    6. El Naschie, M.S., 2008. "Exact non-perturbative derivation of gravity’s G¯4 fine structure constant, the mass of the Higgs and elementary black holes," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 346-359.
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    1. Marek-Crnjac, L., 2009. "A short history of fractal-Cantorian space-time," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2697-2705.
    2. El Naschie, M.S., 2008. "The internal dynamics of the exceptional Lie symmetry groups hierarchy and the coupling constants of unification," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1031-1038.
    3. Giné, Jaume, 2009. "On the origin of the inertia: The modified Newtonian dynamics theory," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1651-1660.
    4. El Naschie, M.S., 2009. "The theory of Cantorian spacetime and high energy particle physics (an informal review)," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2635-2646.
    5. El Naschie, M.S., 2008. "Using Witten’s five Brane theory and the holographic principle to derive the value of the electromagnetic fine structure constant α¯0=1/137," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1051-1053.
    6. Naschie, M.S. El, 2008. "The standard model physical degrees of freedom interpretation of the electromagnetic fine structure coupling α¯o≃1/137," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 609-611.
    7. El Naschie, M.S., 2009. "On zero-dimensional points curvature in the dynamics of Cantorian-fractal spacetime setting and high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2725-2732.

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