Could M4 Kähler force have observable effects?

M⁴ Kähler potential should be felt also by covariantly constant right-handed neutrino so that right-handed neutrino would not completely decouple from gauge interactions. TGD predicts that both quarks and leptons, in particular right- and left-handed neutrinos have an infinite number of color partial waves with CP₂ mass scale. As found, there is a mechanism neutralizing color partial waves of leptons and giving rise to massless neutrinos, which become massive by p-adic thermodynamics. Right-handed covariantly constant neutrinos would already be color singlets and massless so that this mechanism would not be needed. There would however be coupling to the induced M⁴ gauge potential. Could this coupling relate to the poorly understood massivation of neutrinos involving the mixing of right-handed and left-handed neutrinos?

The following simple model makes it possible to estimate the size of the effect of M⁴ Kähler force for elementary fermions at space-time level. Induced Dirac equation is assumed.

1. Both nucleons and leptons create a classical induced M⁴ Kähler potential, which contributes to the U(1) part of the induced electroweak gauge potentials in the background space-time assignable to the nucleus.
2. The gauge forces are felt at the light-like fermion lines at 3-D light-like partonic orbits. A string world sheet connecting say electron and nucleon could mediate the interaction.
3. Consider 1-D light-like fermion line at the partonic orbit of a fermion. Idealize the fermion line as a light-like geodesic line in M⁴× S¹, where S¹⊂ CP₂ is a geodesic circle. 8-D masslessness implies p²- R²ω²=0 (see this), where ω is expected to be the order of the particle mass and characterizes the rotation velocity associated with S¹. A physically motivated guess is that ω is a geometric correlate for the Compton time of the fermion so that fermion can be said to have an internal clock.
4. Consider M4 and CP2 contributions to the Kähler potential. Denote by u the CP2 coordinate serving as a coordinate for the fermion line at the partonic orbit as the interface between Euclidean CP2 type region identifiable as a wormhole contact connecting two Minkowskian space-time sheets and Minkowskian region. The CP2 part of the induced Kähler potential is of order ACP2u ∼ 1/R, where R is CP2 radius. The M4 part of the induced Kähler potential is AM4k∂ mk/∂u ∼ ω ∼ m. For electrons, the ratio of the two contributions is ω R ∼ me/m(CP2) ∼ 10-17 and therefore extremely small. This guarantees that the induced M4 Kähler form has negligible effects.

See the article About Dirac equation in H= M⁴ × CP₂ assuming Kähler structure for M⁴ or the chapter with the same title.

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

For the lists of articles (most of them published in journals founded by Huping Hu) and books about TGD see this.