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  • articleNo Access

    Ratio of Quark Masses in Duality Theories

    We consider N=2 SU(2) Seiberg–Witten duality theory for models with Nf=2 and Nf=3 quark flavors. We investigate arbitrary large bare mass ratios between two or three quarks at the singular points. For Nf=2 we explore large bare mass ratios corresponding to a singularity in the strong coupling region. For Nf=3 we determine the location of both strong and weak coupling singularities that produce specific large bare mass ratios.

  • articleNo Access

    Quantum theory without classical time: Octonions, and a theoretical derivation of the fine structure constant 1/137

    There must exist a reformulation of quantum field theory which does not refer to classical time. We propose a pre-quantum, pre-spacetime theory, which is a matrix-valued Lagrangian dynamics for gravity, Yang–Mills fields, and fermions. The definition of spin in this theory leads us to an eight-dimensional octonionic spacetime. The algebra of the octonions reveals the standard model; model parameters are determined by roots of the cubic characteristic equation of the exceptional Jordan algebra. We derive the asymptotic low-energy value 1/137 of the fine structure constant, and predict the existence of universally interacting spin one Lorentz bosons, which replace the hypothesised graviton. Gravity is not to be quantized, but is an emergent four-dimensional classical phenomenon, precipitated by the spontaneous localisation of highly entangled fermions.