M8-H duality for fermions

M⁸-H duality in bosonic sector is rather well understood but the situation is different in the fermionic sector. The basic guideline is that also fermionic dynamics should be algebraic and number theoretical.

1. Spinors should be octonionic. I have already earlier considered their possible physical interpretation.
2. Dirac equation as linear partial differential equation should be replaced with a linear algebraic equation for octonionic spinors which are complexified octonions. The momentum space variant of the ordinary Dirac equation is an algebrac equation and the proposal is obvious: PΨ=0, where P is the octonionic continuation of the polynomial defining the space-time surface and multiplication is in octonionic sense. The masslessness condition restricts the solutions to light-like 3-surfaces m_klP^kP^l=0 in Minkowskian sector analogous to mass shells in momentum space – just as in the case of ordinary massless Dirac equation. P(o) rather than octonionic coordinate o would define momentum. These mass shells should be mapped to light-like partonic orbits in H.
3. This picture leads to the earlier phenomenological picture about induced spinors in H. Twistor Grassmann approach suggests the localization of the induced spinor fields at light-like partonic orbits in H. If the induced spinor field allows a continuation from 3-D partonic orbits to the interior of X⁴, it would serve as a counterpart of virtual particle in accordance with quantum field theoretical picture.

   See the article Fermionic variant of M⁸-H duality.

   For a summary of earlier postings see Latest progress in TGD.

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