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Yang, C.N. (1987) Square Root of Minus One, Complex Phases and Erwin Schrodinger. In: Kilmister, C.W., Ed., Schrodinger—Centenary Celebration of a Polymath, Cambridge University Press, Cambridge, UK, 53-64.

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• TITLE: From Highly Structured E-Infinity Rings and Transfinite Maximally Symmetric Manifolds to the Dark Energy Density of the Cosmos

  AUTHORS: Mohamed S. El Naschie

  KEYWORDS: Highly Structured Rings, E-Infinity, Loop Spaces, High Energy Physics, Dark Energy, Einstein Relativity, Fractal-Cantorian Spacetime, Nonlinear Dynamics, Quantum Chaos

  JOURNAL NAME: Advances in Pure Mathematics, Vol.4 No.12, December 18, 2014

  ABSTRACT: Starting from well established results in pure mathematics, mainly transfinite set theory, E-infinity algebra over operads, fuzzy manifolds and fuzzy Lie symmetry groups, we construct an exact Weyl scaling for the highly structured E-infinity rings corresponding to E-infinity theory of high energy physics. The final result is an exact expression for the energy density of the cosmos which agrees with previous analysis as well as accurate cosmological measurements and observations, such as COBE, WMAP and Planck. The paper is partially intended as a vivid demonstration of the power of pure mathematics in physics and cosmology.