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E-eight exceptional Lie groups, Fibonacci lattices and the standard model

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  • El Naschie, M.S.

Abstract

This short paper is intended to disclose a most interesting connection between the roots system of the exceptional Lie groups family and the standard model. First an accurate correspondence is found between the roots number of the different groups and the various sections of the mass-spectrum of the standard model and beyond. Second it is shown that the exact gauging of the renormalization group equation is not a logarithmic but rather a fractal scaling related to the geometrical mean of exceptional Lie group family or a Fibonacci line describing the extended standard model. This family may be approximated by (α¯0)(φ3)=32.3606399 as an average where α¯0=137.082033989 is the E-infinity exact value for the inverse fine structure constant and φ=(5-1)/2.

Suggested Citation

  • El Naschie, M.S., 2009. "E-eight exceptional Lie groups, Fibonacci lattices and the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1340-1343.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1340-1343
    DOI: 10.1016/j.chaos.2008.05.015
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    References listed on IDEAS

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    1. Marek-Crnjac, L., 2008. "From Arthur Cayley via Felix Klein, Sophus Lie, Wilhelm Killing, Elie Cartan, Emmy Noether and superstrings to Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1279-1288.
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    Cited by:

    1. 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.
    2. El Naschie, M.S., 2009. "Yang–Mills action as an eigenvalue problem in the theory of elasticity and some measure theoretical interpretation of ‘tHooft’s instanton," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1854-1856.
    3. Marek-Crnjac, L., 2009. "The number of elementary particles in the standard model from purely number theoretical considerations," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1587-1589.
    4. Akbulak, Mehmet & Bozkurt, Durmuş, 2009. "On the order-m generalized Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1347-1355.

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