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Modular groups in Cantorian \(E^{(\infty)}\) high-energy physics. (English) Zbl 1035.83503
Summary: This paper proposes that the geometry and topology of quantum spacetime is shadowed closely by the Möbius geometry of quasi-Fuschian and Kleinian groups and that is the cause behind the phenomena of high-energy particle physics.
In addition, on the large scale measurement of, for instance, the microwave background temperature, the universality of the Merger sponge provides an excellent limit set model for the Charlier–Zeldovich proposal of the fracticality of the universe today and the rather accurate estimate \(T_c=(\ln 20/\ln 3) = 2.726k\).
In particular the paper shows the link between the fix points of the modular groups of the vacuum and the golden mean \(\phi = (1/(1+{\phi})) = (\sqrt 5 - 1)/2\) of \(E^{(\infty)}\) spacetime by analytical continuation of a Möbius transformation.

MSC:
83C45 Quantization of the gravitational field
83F05 Cosmology
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