On track from quantum gravity and its GUT extension towards the general-relativistic version of Feynman graphs

Based on QG, Dirac's special-relativistic formalism is reconstructed for GR. This again is doubling the number of spinor components to 8. This might be another hint towards some U(4,4) structure underlying the conservative U(2,2)-version of QG. Dirac's old, 4-dimensional theory is reproduced in the limit of vanishing dark energy and by the law of great numbers. But his result proves to be inconsistent. Feynman's concept is reanalysed. Its lack of more-body vertices is criticized. A new road map to include GR and the GUT is sketched, rescuing it from the arbitrariness of coupling constants. By QG, both - general relativity and quantum field theories - proved to be applications of 2nd-order Casimir operators. The 3rd- and 4th-order Casimirs, in their lowest approximations are reproducing the old Lorentz invariants, but with spin and booster replaced by total angular momentum and by the total booster of spin and orbit. The exact calculation provides plenty of modifications to be tested by experiment. For more information on QG and GUT see www.q-grav.com.