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58 - Colin B. Hunter 2012
The quaternionic Hopf surface, HL, is associated with a non-compact moduli space, ML, of stable holomorphic SL(2,C) bundles. ML is open in MLc, the corresponding compact moduli space of holomorphic SL(2,C) bundles, and naturally fibers over an open s et of the quaternionic projective line HP^1. We pull back to ML natural locally conformal kaehler and hyperkaehler structures from MLc, and lift natural sub-pseudoriemannian and optical structures from HP^1. Unexpectedly, the holomorphic maps connecting these structures solve the the classical Dirac-Higgs equations of the unbroken Standard Model. These equations include: all observed fermionic and bosonic fields of all three generations with the correct color, weak isospin, and hypercharge values; a Higgs field coupling left and right fermion fields; and a pp-wave gravitational metric. We hypothesize that physics is essentially the geometry of ML, both algebraic (quantum) and differential (classical). We further show that the Yang-Mills equations with fermionic currents also naturally emerge, along with an induced action on the ML structure sheaf equivalent to the time-evolution operator of the associated quantum field theory.
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