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### More about the Construction of Scattering Amplitudes in TGD Framework

#### Abstract

During the 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 #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 (SH) are discussed. What is found that number theoretic view justifies the assignment of 2-D action to string world sheets. Does the 2-D action appear as a primary term in the action or emerge dynamically as SH encourages to think? The latter option turns out to be the correct one. String world sheets can be regarded as 2-D edges/folds of 4-D space-time. 2-D edges would be minimal surfaces and carry a singular part of 4-D action. Also partonic 2-surfaces would form analog of foam with network defined by nodes connected by edges (geodesic lines), as the proposal for symplectic QFT as part of quantum TGD indeed suggests. This picture has interpretation as a (generalized) calibration that I suggested for long time ago. The notion of discrete coupling constant evolution, quantum criticality, and number theoretical arguments lead in twistor Grassmann approach to an extremely simple proposal: the loop corrections to scattering amplitudes must vanish so that the twistorial recursion formulas for the scattering amplitudes trivialize. This requires that unitarity cuts are replaced with poles of finite width: scattering amplitude would reduce to a sum over resonance poles just as was assumed in the dual resonance models based on stringy picture, which later led to super string models. Superstring models failed: could it be that dual resonance models were much close to reality than superstrings and M-theory? TGD suggests that this might be the case.