Does Riemann Zeta Code for Generic Coupling Constant Evolution?

Abstract

A general model for the coupling constant evolution is proposed. The analogy of Riemann zeta and fermionic zeta ζ_F(s)/ ζ_F(2s) with complex square root of a partition function natural in Zero Energy Ontology suggests that the poles of ζ_F(ks), k=1/2, correspond to complexified critical temperatures identifiable as inverse of Kahler coupling strength itself having interpretation as inverse of critical temperature. One can actually replace the argument s of ζ_F with Mobius transformed argument w=(as+b)/(cs+d) with a,b,c,d real numbers, rationals, or even integers. For αK w=(s+b)/2 is proper choices and gives zeros of ζ(s) and s=2-b as poles. The identification αK= αK_U(1) leads to a prediction for α_em, which deviates by 0.7 per cent from the experimental value at low energies (atomic scale) if the experimental value of the Weinberg angle is used. The conjecture generalizes also to weak, color and gravitational interactions when general Mobius transformation leaving upper half-plane invariant is allowed. One ends up with a general model predicting successfully the entire electroweak coupling constant evolution successfully from the values of fine structure constant at atomic or electron scale and in weak scale.