About the Relationship of Electroweak and Strong Interactions in the TGD Universe: Part I

The following represents the abstract of the 1^st part of a 3-part article summarizing the view about the relationship of electroweak and strong interactions in the TGD Universe. This view has been developed together with Martin Ebner during the last almost four months. The model has evolved by trial and error process from a general view about weak and strong interactions as different aspects of color interactions coded by CP₂ geometry. Without Martin Ebner and his two AI agents the work would not have been possible.

The purpose of this three-part article is to develop a more detailed view of the relationship between electroweak and strong interactions at the level of the embedding space H. In the first part of the article the general vision is described. In the second part a concrete model for the Weinberg angle is developed, leading to a vision about the relationship of weak and strong interactions in the TGD framework. In the third part the masses of W and Z⁰ and their ratio are estimated, and questions related to the relationship of weak and strong interactions are discussed.

The TGD view of electroweak and strong interactions based on CP₂ geometry allows to interprete see strong and weak interactions as different aspects of color interaction During last almost four months we have worked together with Martin Ebner a view about how this view relates to the standard model.

My own AI skills are meager and at this age computation is far from being a pleasure. Martin together with two AI agents has made possible to develop by trial an error method a model free of any obvious problems. The model leads to a generalization of Weinberg rotation. Excellent estimates for the basic coupling parameters of the standard model and for the W/Z mass ratio emerge.

The following is the abstract of the firest part of the article having 3 parts.

The purpose of this three-part article is to develop a more detailed view of the relationship between electroweak and strong interactions at the level of the embedding space H. In the first part of the article the general vision is described. In the second part a concrete model for the Weinberg angle is developed, leading to a vision about the relationship of weak and strong interactions in the TGD framework. In the third part the masses of W and Z⁰ and their ratio are estimated, and questions related to the relationship of weak and strong interactions are discussed.

General view. Quantum TGD involves three levels corresponding to embedding space H=M⁴× CP₂, space-time X⁴ and “world of classical worlds” (WCW). Holography principle at X⁴ level implies the absence of path integral and related divergence problems. Holography = holomorphy (H-H) principle allows an exact solution of field equations. Also Lagrangian minimal surfaces are allowed as candidates for preferred extremals.

Bosons are not primary fields and correspond at H and WCW levels to bound states of fermions. At H and X⁴ level bosons correspond to induced spinor connections and apparently only electroweak gauge bosons are present. These couplings however involve implicitly vector boson couplings identified as U(1) counterparts of gluons by electric-magnetic duality. The challenge is to identify the gluon propagators at the level of X⁴.

Fermions at the H level are identified as modes of H spinor fields forming a hierarchy of color multiplets. This predicts a hierarchy of standard model physics. At the X⁴ level fermions correspond to induced spinor fields.

Construction of scattering amplitudes. Interactions are contact interactions with contacts defined by the 2-D string world sheets as intersections of space-time surfaces, including self intersections. Fermion lines correspond to intersections of string world sheets and partonic orbits.

Zero energy ontology (ZEO) and the associated mild classical non-determinism are fundamental. The loci of classical non-determinism as intersections of 3-D edges of space-time with 3-D partonic orbits define partonic 2-surfaces as geometric vertices. Feynman graphs are replaced with analogs of Brownian motion for 3-surfaces and associated fermion lines. Fermion propagators are free propagators in H. Bosonic propagators correspond to WCW correlation functions.

Q CD serves as a role model. The notions of fragmentation and hadronization are generalized. H level corresponds to observed hadrons and leptons. At X⁴ level quark gluon plasma is replaced by induced spinor fields for quarks and leptons. ZEO gives rise to statistical aspects appearing also in QCD.

Standard model and TGD. The Higgs mechanism is a key element of the standard model. p-Adic thermodynamics replaces it at the level of WCW. At the X⁴ level massivation is described in terms of warping distinguishing between GRT and TGD.

Kähler-Chern-Simons action (KCS) and corresponding modified Dirac action define the dynamics for the partonic orbits. M⁴ possesses an analog of Kähler structure and contributes to this action an additive part.

Color confinement involves two steps. First color triplets/singlets are formed from quark/leptonic color multiplets and then color triplets form hadrons. The color information is coded by WCW wave functions for the position of the fermion line and its edge at the partonic 2-surface. The 3 members of the color triplet are associated with the 3 coordinate patches of CP₂.

The condition stating that the emission amplitude for conformal photons vanishes is postulated and states conformal invariance. Electric-magnetic duality states that U(1) interaction at X⁴ level corresponds to color interaction of QCD such that the two coupling strengths are inverses of each other. A model for WCW wave functions as monopole harmonics at partonic 2-surfaces leads to a 3-D generalization of Weinberg rotation and an estimate of the Weinberg angle, identification of strong and weak interactions as parts of color interaction and estimate of the strong coupling strength.

See the article About the Relationship of Electroweak and Strong Interactions in the TGD Universe: Part I 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.

Source: https://matpitka.blogspot.com/2026/10/about-relationship-of-electroweak-and.html