Modular groups in Cantorian E(∞) high-energy physics

This paper proposes that the geometry and topology of quantum spacetime is shadowed closely by the Mobius 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)) = (root5- 1)/2 of E-(infinity) spacetime by analytical continuation of a M6bius transformation. (C) 2002 Elsevier Science. Ltd. All rights reserved.