Analog with Higgs mechanism and 3-D singular surfaces as analogs of soap bubbles

The vertices for the fermion pair creation are located 3-D singular surfaces X³ at which the conformal invariance fails. Can one say anything interesting about these 3-surfaces or even find a possible analogy with the existing physics? The idea that the trace of the second fundamental form which becomes singular at X³ relates closely to Higgs has been around from the beginning of TGD. In the following I want to show that this idea has finally found a precise form.

1. The trace of the 8-D second fundamental form defines a generalized local acceleration orthogonal to the space-time surface X⁴, which vanishes almost everywhere by the minimal surface property. It is non-vanishing only at the 3-D singularities X³ representing edges of X⁴. The vertices for fermion pair creation as edges of fermion lines are assigned to intersections of string world sheets with X³ in the intersection of intersecting space-time surfaces with the same Hamilton-Jacobi structure.
2. The second fundamental form is analogous to generalized Higgs, call it H, with the CP₂ part being group theoretically like the ordinary Higgs field and indeed causing a violation of the conservation of M⁴ chirality. The M⁴ part is identifiable as ordinary local acceleration. The generalized acceleration has the dimension of inverse length, that is the dimension of mass divided by Planck constant. Higgs vacuum expectation corresponds to the fermion mass in the standard model. Is this true also in TGD?
3. By both Dirac equation in H and Dirac equation with M⁴ Kähler form for CD the fermions are massless in 8-D sense. If the additivity of M⁴ mass squared, identified as a conformal weight, is assumed, all many-fermion states have a vanishing mass squared in 8-D sense so that the total M⁴ mass squared equals to CP₂ mass squared proportional to color Casimir. It vanishes for color singlets but has a CP₂ mass scale as a natural unit for colored states.
4. If M⁴- and CP₂ parts of the generalized Higgs have magnitude equal to the mass squared of the particle, quantum-classical correspondence is realized. p-Adic thermodynamics would predict M⁴ mass squared (see this). At X³, the condition a_M⁴ = m/h_eff for the M⁴ acceleration, where m the mass of the particle, would be satisfied. Conformal invariance would fail X³ but the 8-D masslessness would remain true. Local mass value depends on the point of X³ unless the magnitudes of a_M⁴ and a_CP2 are constant. The direction of 8-D acceleration is orthogonal to X⁴ and also X³.
5. What could be the physical interpretation for the possible constant magnitude of M⁴ and CP₂ accelerations? Isometrically embedded 3-sphere in E⁴ represents a basic example of this kind of surface. Also a soap bubble is an example of a surface with constant value of local acceleration. The surface tension corresponds to the local acceleration and is proportional to the pressure difference. This suggests that the 3-D singularities are analogous to the surfaces of 3-D soap bubbles.

See the article Comparing the S-matrix descriptions of fundamental interactions provided by standard model and TGD 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.