Mathematical foundation of E-Infinity via Coxeter and reflection groups

Using various results from the abstract theory of Coxeter and reflection groups, we give concise and elegant mathematical foundation for the fundamental equation of E-Infinity theory.     

On quarks confinement and asymptotic freedom

We review briefly previous works on quarks confinement and asymptotic freedom. Subsequently we introduce the magnetic monopole pair inverse coupling in analogy to the Cooper pairs electromagnetic inverse fine structure constant .

Finally, we show that confinement is absolute at certain energy scale limit where the Planck energy is M_p = (10)¹⁹ Gev and the expectation value of a number of generation equal to 16 + k plays a crucial role. It is important to note that is de facto replaced by and . The phenomena discussed here have a classical analogy in the engineering theory of plasticity called strain hardening or negative super spring.     

From pointillism to E-infinity electromagnetism

Pretty much like in a pointillism masterpiece of say Georges Seurat or Paul Signac, quantum space-time, which is in reality a collection of transfinite discrete set of points, appears when observed at a distance to be a nowhere disjoined continuum. This geometry which is best described by its Hausdorff dimension leads us ultimately to a radical change of some of our most basic mathematical assumptions with regard to the corresponding symmetry groups. Thus instead of being restricted to an integer value of the order of these symmetry groups, it seems natural to extend this order to the realm of irrational transfinite numbers. This step is not as strange as it may seem when we consider the role played by the factorial function n! in elementary group theory and its extension for non-integer value of n using the well-known Gauss’ Gamma function.

Proceeding in this way, we find that the space-time of E-infinity theory constitutes a transfinite pointillism setting in which all fundamental interactions could be accounted for via the corresponding transfinite order of its symmetry groups and finally we find a conservation equation from which the exact inverse fine structure constant may be accurately determined.     

A P-Brane vindication of the two Higgs-doublet minimally super-symmetric standard model and related issues

The two-Higgs doublet MSSM predicts three neutral and two charged Higgs particles. The present work gives a vindication of this model based on a P-Brane model in eleven dimensions. Subsequently, we give alternative derivations using various ideas from the theory of maximally symmetric spaces and E-Infinity theory.     

Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics

The geometry of classical platonic solids and their generalization to four-dimensional fuzzy polytopes are considered. Subsequently it is shown how the so obtained relationships and the associated symmetry groups are related to high energy particle physics. In particular the topology of a fuzzy Dodecahedron and four-dimensional polytopes are used to give information about the elementary particles content of the standard model of high energy physics.     

Wild topology, hyperbolic geometry and fusion algebra of high energy particle physics

The relation between Wild Topology, Hyperbolic Geometry and Fusion Algebra on the one side and the charge and coupling constants of the standard model and quantum gravity on the other is examined.

The close connection found between theory and the Topological theory of four manifolds as well as the theory of fundamental groups is elucidated using various classical theories and recent results due to Antoine, Wada, Alexander, Klein, Kummer, Freedman, Kaufmann, Witten, Jones and Connes.     

The theory of Cantorian spacetime and high energy particle physics (an informal review)

The paper gives a rather detailed introduction and up to date review of the main concepts and ideas upon which the theory of fractal-Cantorian spacetime is based.     

Nash's surface and the space of quantum scale

We draw some connections between Nash's theorem on imbedding of Riemannian manifolds and space and speculate on further connections to fractal spacetime and high energy physics. It is conjectured that 26 dimensions are required for imbedding a Menger sponge of arbitrary large size into an arbitrary small portion of the 26 dimensional space. We further conjecture that the 26 dimensions on their own already imply the fracticality of the surfaces imbedded into such a space and allow for a non-intuitive results similar to the Banach–Tarski decomposition theorem.