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From symmetry to particles

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  • El Naschie, M.S.

Abstract

The notion of a particle-like state emerging from a symmetry breaking is given five corresponding pictures. We start from a geometrical picture in two dimensions involving a modular curve constructed using 336 triangles. The same number of building blocks is found again, this time as 336 contact points in the ten dimensional space of super string theory in the context of the largest kissing number of lattice sphere packing. The next corresponding representation is an abstract one pertinent to the order of the simple linear Lie group SL(2,n) in seven dimensions (n=7) which leads to 336 symmetries. Subsequently a tensorial picture is given using the Riemannian tensor of relativity theory but this time in an eight dimensional space (n=8) for which the number of independent components is again 336. Finally we use a physical string theory related picture in the 12 dimensions of F theory to find 336 moduli space dimensions representing the instanton cells of our theory.

Suggested Citation

  • El Naschie, M.S., 2007. "From symmetry to particles," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 427-430.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:427-430
    DOI: 10.1016/j.chaos.2006.09.016
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. El Naschie, M.S., 2007. "Estimating the experimental value of the electromagnetic fine structure constant α¯0=1/137.036 using the Leech lattice in conjunction with the monster group and Spher’s kissing number in 24 dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 383-387.
    5. 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.
    6. El Naschie, M.S., 2006. "Elementary prerequisites for E-infinity," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 579-605.
    7. Naschie, M.S. El, 2006. "Holographic correspondence and quantum gravity in E-infinity spacetime," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 871-875.
    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., 2005. "Determining the number of Higgs particles starting from general relativity and various other field theories," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 711-726.
    10. El Naschie, M.S., 2006. "On two new fuzzy Kähler manifolds, Klein modular space and ’t Hooft holographic principles," Chaos, Solitons & Fractals, Elsevier, vol. 29(4), pages 876-881.
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    Cited by:

    1. Kocer, E. Gokcen & Tuglu, Naim & Stakhov, Alexey, 2009. "On the m-extension of the Fibonacci and Lucas p-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1890-1906.
    2. El Naschie, M.S., 2007. "From pointillism to E-infinity electromagnetism," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1377-1381.
    3. Gottlieb, I. & Agop, M. & Enache, V., 2009. "Games with Cantor’s dust," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 940-945.
    4. Agop, M. & Paun, V. & Harabagiu, Anca, 2008. "El Naschie’s ε(∞) theory and effects of nanoparticle clustering on the heat transport in nanofluids," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1269-1278.
    5. El Naschie, M.S., 2008. "Noether’s theorem, exceptional Lie groups hierarchy and determining 1/α≅137 of electromagnetism," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 99-103.
    6. Kılıç, Emrah, 2009. "The generalized Pell (p,i)-numbers and their Binet formulas, combinatorial representations, sums," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 2047-2063.
    7. 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.
    8. Kilic, E. & Stakhov, A.P., 2009. "On the Fibonacci and Lucas p-numbers, their sums, families of bipartite graphs and permanents of certain matrices," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2210-2221.
    9. Ekici, Erdal & Noiri, Takashi, 2009. "Decompositions of continuity, α-continuity and AB-continuity," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2055-2061.
    10. Akbulak, Mehmet & Bozkurt, Durmuş, 2009. "On the order-m generalized Fibonacci k-numbers," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1347-1355.
    11. Agop, M. & Chicos, Liliana & Nica, P., 2009. "Transport phenomena in nanostructures and non-differentiable space–time," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 803-814.
    12. Agop, M. & Murgulet, C., 2007. "Ball lightning as a self-organizing process of a plasma–plasma interface and El Naschie’s ε(∞) space–time," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 754-769.

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