During years I have considered several proposals for S-matrix in TGD framework - perhaps the most realistic proposal relies on the generalization of twistor Grassmann approach to TGD context. There are several questions waiting for an answer. How to achieve unitarity? What it is to be a particle in classical sense? Can one identify TGD analogs of quantum fields? Could scattering amplitudes have interpretation as Fourier transforms of n-point functions for the analogs of quantum fields?
Unitarity is certainly the issue number 1 and in the sequel almost trivial solution to the unitarity problem based on the existence of super-symplectic transformations acting as isometries of "world of classical worlds" implying infinite number of conserved Noether charges in turn guaranteeing unitarity. Also quantum classical correspondence and the role of string world sheets for strong form of holography are discussed. What is found that number theoretic view justifies the assignment of action to string world sheets.
See the chapter The Recent View about Twistorialization in TGD Framework or the article More about the construction of scattering amplitudes in TGD framework .