TGD View About Coupling Constant Evolution

Abstract

New results related to the TGD view about coupling constant evolution are discussed. The results emerge from the discussion of the recent claim of Atyiah that fine structure constant could be understood purely mathematically. The new view allows to understand the recently introduced TGD-based construction of scattering amplitudes based on the analog of micro-canonical ensemble as a cognitive representation for the much more complex construction of full scattering amplitudes using real numbers rather than p-adic number fields. This construction utilizes number theoretic discretization of space-time surface inducing the "world of classical worlds" (WCW) and makes possible adelization of quantum TGD. The condition determining coupling constant evolution in the hierarchy of extensions of rationals defining that of adeles is extremely simple: exp(S)=1, where S is the complex action determining space-time surface as preferred extremal. The condition allows to circumvent the difficulties caused to the adelization by the fact that exp(S) need not belong to the extension of rationals considered. The approach is also related to the view about coupling constant evolution based on the inclusions of hyper-finite factors of type II₁, and it is proposed that Galois group replaces discrete subgroup of SU(2) leaving invariant the algebras of observables of the factors appearing in the inclusion.