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Finally!

Wednesday, July 30, 2025 0:49

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It is not an exaggeration to say that the 47 year lasting work to develop the basic vision behind TGD to a mathematical theory with a precise physical interpretation is in some sense finished. Because of the fractality, the emerging theory solves numerous anomalies and makes dramatic predictions in all scales. The next step is to transform the theory to a calculational apparatus but this requires a collective effort of both mathematicians and physicists.

The last steps in the process made transparent the amazing simplicity of the overall picture.

The study of the solution spectrum of Dirac equations in the imbedding space H=M⁴×CP₂ and space-time surface X⁴ have led to a quite dramatic increase of the understanding of how TGD view of standard model physics and gravitation differs from standard view.

Color confinement can be understood directly from the study of Dirac equation in H with M⁴ endowed with Kähler structure and electroweak and strong interactions can be seen as different aspects of the same interaction. All interactions reduce to the dynamics of 3-surfaces obeying holography = holomorphy principle and by general coordinate invariance only 4 H-coordinates define the primary dynamical variables at the fundamental level.

Color partial waves in H are analogous to angular momentum states and since the electroweak group can be regarded as a subgroup of SU(3), electroweak quantum numbers can be regarded as color quantum numbers analogous to spin. “Strong-electroweak” is completely analogous “orbital angular momentum-spin”.

CP₂= SU(3)/U(2) states that also geometrically U(2) acts like a gauge group, whereas SU(3) as a whole is not a gauge group. This sharply distinguishes standard model and its generalizations from TGD.

By holography= holomorphy principle, X⁴ can be seen as a generalization of a point-like particle and X⁴ spinor modes are analogous to the spin states of a point-like particle. The interaction of two space-time surfaces occurs in the intersection of the particle-like 4-surfaces, which for identical H-J structures consists of string world sheets. This is nothing but the analog for the interaction of point-like particles occurring only when they are at the same point.

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.

Source: https://matpitka.blogspot.com/2025/07/finally.html

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