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preprint: January 1, 2008, 19 pages, to be submitted after updates and additions

Abstract:

A novel Algebraic Topology approach to Supersymmetry (SUSY) and Symmetry Breaking in Quantum Field and Quantum Gravity theories is presented with a view to developing a wide range of physical applications, such as: controlled nuclear fusion and other nuclear reactions studies in quantum chromodynamics, nonlinear physics at high energy densities, dynamic Jahn-Teller effects, superfluidity, high temperature superconductors, multiple scattering by molecular systems, molecular or atomic paracrystal structures, nanomaterials, ferromagnetism in glassy materials, spin glasses, quantum phase transitions, and supergravity. This approach requires a unified conceptual framework that utilizes extended symmetries and quantum groupoid, algebroid and functorial representations of non--Abelian higher dimensional structures pertinent to quantized spacetime topology and state space geometry of quantum operator algebras. The relevance of our approach to extended quantum symmetries and their associated representations in locally covariant General Relativity theories that are consistent with nonlocal quantum field theories are also presented. http://www.bangor.ac.uk/~mas010/brownpr.html

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Open access: http://www.bangor.ac.uk/~mas010/brownpr.html

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