On TGD Counterparts of Twistor Amplitudes: Part I

Abstract

This article is the first part of the article devoted the construction of scattering amplitudes in the TGD framework based on twistor approach. The twistor lift of TGD, in which H=M⁴ x CP₂ is replaced with the product of twistor spaces T(M⁴) and T(CP₂), and space-time surface X⁴ ⊂ H with its 6-D twistor space as 6-surface X⁶ ⊂ T(M⁴) x T(CP₂), is now a rather well-established notion and M⁸-H duality predicts it at the level of M⁸. Number theoretical vision involves M⁸-H duality. At the level of H the quark mass spectrum is determined by the Dirac equation in H. In M⁸ mass squared spectrum is determined by the roots of the polynomial P determining space-time surface and are in general complex.  By Galois confinement the momenta are integer valued when p-adic mass is used as a unit and mass squared spectrum is also integer valued.  This raises hope about a generalization of the twistorial construction of scattering amplitudes to TGD context. It is always best to start from a problem and the basic problem of the twistor approach is that physical particles are not massless.