Stringy Scattering Amplitudes in Twistor Grassmannian Approach: TGD Perspective

Abstract

A generalization of twistor Grassmannian approach defines a very promising vision about the construction of generalized Feynman diagrams. Since particles are replaced with 3-D surfaces and since string like objects emerge naturally in TGD framework, one expects that scattering amplitudes define a generalization of twistor Grassmannian amplitudes with a generalized Yangian symmetry. The realization of this approach has been however plagued by long-standing problems. SUSY in some form seems to be strongly supported by theoretical elegance and TGD indeed suggests a good candidate for a broken SUSY realized in terms of covariantly constant right-handed neutrino not requiring Majorana spinors. Separate conservations of baryon and lepton number imply that super-generators carry quark or lepton number. This has been the main obstacle in attempts to construct stringy amplitudes. In this article it is found that this obstacles can be overcome and that stringy approach is forced both by the TGD view about physical particles and by the cancellation of UV and IR divergences. Also the planarity restriction emerges automatically in stringy approach. Absolutely essential ingredient is that fundamental fermions can be regarded as massless on-shell fermions having non-physical helicity with propagator replaced with its inverse: this representation follows by performing the integration over the virtual four-momentum squared using residue calculus.