Abstract
After the discovery of the slow growth of loop corrections with cutoff energy and the possibility of renormalization of the Lagrangians, the main unsolved problem of quantum field theory remained ultraviolet divergences, and the long search for a physical mechanism making regularization finite was unsuccessful. The main reason for this was the hasty conclusion that known phenomena were already taken into account and, as the result, the solution has been associated with radical hypotheses only. It is shown in the paper that the desired mechanism already existed initially and this is the gravitational time dilation. The standard treatment included high-energy quanta, but did not take into account their gravity, and in attempts to take into account it, gravity was considered only as one of the fields. But external gravitational field of quanta also slows down the local proper times in terms of the world time t of distant observers. It is shown that at the Planck length, the gravitational radius of the Planck energy quanta, all processes freeze and therefore do not contribute to the S-matrix defined on the hypersurface of simultaneity t = const. The freezing of quantum fluctuations means a strong redshift of high frequencies up to their vanishing and thus gravitation of quanta leads to their self-regularization. The nonlinearity of fields increases the gravitational effects, and hence the freezing, which even more reduces the high energy contributions. The ultraviolet finiteness of the loop corrections makes consistent non-renormalizable models too, if these corrections are small. For gauge fields and quantum gravity, the invariant Planck cutting of the integrals gives upper limits for the loop diagram corrections, which appear small and the perturbation theory series converge. The consequences of the finiteness of the Standard Model and quantum gravity are discussed.
