A Renormalisable Cosmodynamic Model

Abstract

The fermionic gyromagnetic ratio g= 2 of the Kerr-Newman spacetime cannot be a computational "coincidence". This naturally immerges in a four dimensional generally covariant modified Yang-Mills action, which depends on the lorentzian complex structure of spacetime and not its metric. This metric independence makes the model renormalizable. It is a counter example to the general belief that "string theory is the only selfconsistent quantum model which includes gravity". The other properties of the model are phenomenologically very interesting too. The modified Yang-Mills action generates a linear potential, instead of the Coulomb-like (1/r) potential of the ordinary action. Therefore the Yang-Mills excitations must be perturbatively confined. This separates the solutions of the model into the vacuum bosonic sector of the periodic configurations, the "leptonic" sector with fermionic solitons and their gauge field excitations, the "hadronic" sector. Simple integrability conditions of the pure geometric equations imply a limited number of "leptonic" and "hadronic" families. The geometric surfaces are generally inside the SU(2,2) classical domain. Soliton spin and gravity measure how much the surface penetrates inside the classical domain. The i0 point of infinity breaks the SU(2,2) symmetry down to the Poincare and dilation groups. A scaling breaking mechanism is presented. Hence the pure geometric modes and asymptotically flat solitons of the model must belong to representations of the Poincare group. The metrics compatible to the lorentzian complex structure are induced by a Kaehler metric and the spacetime is a totally real lagrangian submanifold of a Kaehler manifold. This opens up the possibility to use the geometric quantization directly to the solitonic surfaces of the model, considering their corresponding Kaehler symplectic manifold as their phase space.