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Deriving the largest expected number of elementary particles in the standard model from the maximal compact subgroup H of the exceptional Lie group E7(-5)

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  • El Naschie, M.S.

Abstract

The maximal number of elementary particles which could be expected to be found within a modestly extended energy scale of the standard model was found using various methods to be N=69. In particular using E-infinity theory the present Author found the exact transfinite expectation value to be 〈N〉=α¯o/2≅69 where α¯o=137.082039325 is the exact inverse fine structure constant. In the present work we show among other things how to derive the exact integer value 69 from the exceptional Lie symmetry groups hierarchy. It is found that the relevant number is given by dimH=69 where H is the maximal compact subspace of E7(-5) so that N=dimH=69 while dimE7=133.

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  • El Naschie, M.S., 2008. "Deriving the largest expected number of elementary particles in the standard model from the maximal compact subgroup H of the exceptional Lie group E7(-5)," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 956-961.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:4:p:956-961
    DOI: 10.1016/j.chaos.2008.06.004
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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. El Naschie, M.S., 2005. "On 336 kissing spheres in 10 dimensions, 528 P-Brane states in 11 dimensions and the 60 elementary particles of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 24(2), pages 447-457.
    4. El Naschie, M.S., 2008. "Symmetry group prerequisite for E-infinity in high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 202-211.
    5. 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.
    6. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    7. El Naschie, M.S., 2006. "Topics in the mathematical physics of E-infinity theory," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 656-663.
    8. El Naschie, M.S., 2006. "Holographic dimensional reduction: Center manifold theorem and E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 816-822.
    9. El Naschie, M.S., 2006. "Superstrings, entropy and the elementary particles content of the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 48-54.
    10. El Naschie, M.S., 2007. "The elementary particles content of quantum spacetime via Feynman graphs and higher dimensional polytops," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 1-4.
    11. El Naschie, M.S., 2006. "Elementary number theory in superstrings, loop quantum mechanics, twistors and E-infinity high energy physics," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 297-330.
    12. El Naschie, M.S., 2007. "Gauge anomalies, SU(N) irreducible representation and the number of elementary particles of a minimally extended standard model," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 14-16.
    13. El Naschie, M.S., 2006. "Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1025-1033.
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    Cited by:

    1. Elokaby, Ayman, 2009. "Knot wormholes and the dimensional invariant of exceptional Lie groups and Stein space hierarchies," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1616-1618.
    2. El Naschie, M.S., 2009. "Knots and exceptional Lie groups as building blocks of high energy particle physics," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1799-1803.
    3. El Naschie, M.S., 2008. "An energy balance Eigenvalue equation for determining super strings dimensional hierarchy and coupling constants," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1283-1285.
    4. El Naschie, M.S., 2009. "Reasons why the current CERN experiment should discover at least one new spin zero elementary particle and probably several others," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2838-2841.
    5. El Naschie, M.S., 2008. "Anomalies free E-infinity from von Neumann’s continuous geometry," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1318-1322.
    6. El Naschie, M.S., 2009. "On the Witten–Duff five Branes model together with knots theory and E8E8 super strings in a single fractal spacetime theory," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2018-2021.
    7. Elmali, Ceren Sultan & Uğur, Tamer, 2009. "Fan-Gottesman compactification of some specific spaces is Wallman-type compactification," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 17-19.
    8. El Naschie, M.S., 2008. "Fuzzy multi-instanton knots in the fabric of space–time and Dirac’s vacuum fluctuation," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1260-1268.
    9. 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.
    10. Halayka, S., 2009. "Some visually interesting non-standard quaternion fractal sets," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2842-2846.
    11. El Naschie, M.S., 2009. "Kac–Moody exceptional E12 from simplictic tiling," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1569-1571.

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