Thursday, September 27, 2012

Electron as a trefoil or something more general?

The progress in the understanding of the modified Dirac equation led to the conclusion that the mere conservation of em charge in spinorial manner rather than from theorem of Gauss allows to conclude that the solutions of the modified Dirac equation must be localized at string world sheets and partonic 2-surfaces: right-handed neutrino is expection and delocalized into entire space-time surface. Looking more closely the implications of this led to the conclusion that every ordinary elementary fermion is accompanied by closed string. Ordinary elementary bosons can be accompanied by two such strings. If light-like wormhole throat orbots carry several fermions one can have several closed strings. These closed strings can get knotted and braided. I do not bother to type more but attach the
abstract of a little article Electron as a trefoil or something more general?.

There have been suggestions that elementary particle could be braided structure and that standard model quantum numbers could be reduced to topology. In TGD framework this option does not look plausible. The braiding at the level of wormhole throat orbits is however in principle possible but need not be significant for the known elementary particles. In TGD framework elementary particle is identified as a closed Kähler magnetic flux tube carrying monopole magnetic field. This flux tube is accompanied by a closed string representing the end of string world sheet carrying induced spinor field. This string can be homologically non-trivial curve and can also get knotted. Bosons even braiding becomes possible and in the general case knotting, braiding, and non-trivial homology are possible. Therefore an extremely rich topological structure is predicted, which might corresponds to relatively low energy scale. Topological sum for knots and reconnection are the basic topological reactions for these strings and can change the knotting of the string. These reactions represent basic vertices for closed strings so that closed string model could give at least idea about the dynamics of knotting and un-knotting.

For details and background see the chapter Knots and TGD, or the already mentioned article .


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