On the TGD Based Notions of Mass of Twistors & Hyperbolic Counterpart of Fermi Torus

Abstract

The notion of mass in the TGD framework is discussed from the perspective of M⁸ - H duality. Also the TGD based notion of twistor space is considered at concrete geometric level. This discussion justifies the proposed concrete solution of a technical problem related to the proposed identification of scattering amplitudes reducing particle reactions to a re-arrangement of the fermions forming Galois singlets to new Galois singlets. The third topic of this article is the hyperbolic generalization of the Fermi torus to hyperbolic 3-manifold H³/Γ. Here H³ = SO(1,3)/SO(3) identifiable the mass shell M⁴⊆ M⁸ or its M⁸ - H dual in H = M⁴ x CP₂. Γ denotes an infinite subgroup of SO(1,3) acting completely discontinuously in H³. For virtual fermions also complexified mass shells are required and the question is whether the generalization of H³/Γ, defining besides hyperbolic 3-manifold also tessellation of H³ analogous to a cubic lattice of E³.