## Derivation of a Chiral (Spin(3)*su(2)*u(1))/z_3 Quantum Field from Kaluza-Klein Theory

**Authors:** Michael James Goodband

A geometric theory in 10+1 dimensions is developed starting from a transition S^{10} → S^{3}×S^{7} followed by dynamical compactification in which S^{7} becomes the compactified particle dimensions in a Kaluza-Klein theory, and the spatial S^{3} inflates. The closed space acquires a vacuum winding π_{7}(S^{3})=π_{4(S3)=Z2 with Spin(3), SU(2), U(1) eigenvalues (0,–½ 1) and chirality Z2 = {L, R}. This vacuum breaks the symmetry of the particle space SU(4)/SU(3) ≅ S7 to (Spin(3)⊗SU(2)⊗U(1))/Z3 giving 12 topological monopoles (π6(S2) = Z3×Z4) with spin ½ giving 3 families of 4 fermionic monopoles that split into Spin(3) coloured and colourless SU(2) doublets with the same charges as the fundamental particles. Topological conditions in the classical theory give a definition of Planck's constant ħ=c3χ2/G as the physical scale of the topological spin charge, and define the Weinberg angle as tan2θ_W=5/16. Closed formulae for e, g, g', mZ, mW, mH are derived in the classical theory. The topological monopoles take the form of rotating compactified black holes in the dimensionally reduced theory, where their ergo-region can trap virtual-radiation sufficient to cancel the rest mass of the black hole. This leads to the derivation of a quantum field theory for the topological monopoles where the Kaluza-Klein dimensional reduction gives a Lagrangian containing the terms of the Standard Model, including a quartic scalar field term which gives the coupling constant value λ=1/8 for the Higgs term.
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**Comments:** 31 Pages.

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### Submission history

[v1] 2012-09-12 10:20:28

[v2] 2012-12-20 09:45:06

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