TGD counterpart of Feynman diagrammatics with application to QFT limit and CP violation

Concerning the construction of scattering amplitudes, the M⁸ approach provides a very nice picture (see this) about the scattering amplitudes in the momentum space representation in the fermionic sector involving only 2-vertices identifiable in terms of analog of Brownian motion. This representation is however restricted to scattering amplitudes for a fixed space-time surface. The full scattering amplitudes require a functional integral over the WCW and this gives rise to the counterparts of bosonic propagators. In this article this aspect will be discussed.

The QFT limit of TGD must exist and emerge naturally from the full theory. This gives strong hints. One should understand the TGD counterparts of various notions such as fermion lines, vertices, fermion pair creation, and loops. The basic idea is simple: n-point functions of QFT generalize to n-point functions for the WCW spinor field at points which correspond to the 3-D edges of the space-time defining the vertices. Edges are 3-D delta function singularities for the trace of the second fundamental form for space-time surface as minimal surface, vanishing elsewhere and having an interpretation as a generalized acceleration and generalized classical Higgs field. This is true for any general coordinate invariant action constructible in terms of the induced geometry and has interpretation as universality associated with 4-D quantum criticality.

A key role is played by the notion of exotic smooth structure (see this, this, and this), which are possible in TGD (see this, this, this, and this). Exotic smooth structure is realized in terms of edges of the space-time allowing V-shaped fermion lines. In time direction this corresponds to a creation of a fermion pair. Most importantly, it is also possible to have finite fermion loops in which the fermion turns backwards in time and returns back along the same line.

This picture is applied to CP violation, whose understanding relies on loops. TGD predicts an entire hierarchy of standard model physics. A given standard model physics corresponds to color multiplets associated with a given mode of the Dirac equation in H (see this and this). To each multiplet one can assign a p-adic mass scale. The local transition to a scaled variant of hadron physics with a larger p-adic mass scale contributes to the CP violation. The CP violation can be assigned to the instanton part of the Kähler action giving rise to Kähler-Chern-Simons term assignable to the light-like partonic orbit carrying the fermion line (see this and this).

See the article TGD counterpart of Feynman diagrammatics with application to QFT limit and CP violation 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.