Geometry of the divergences problem in QFT

Abstract

The divergences problem in QFT should be overcame presumably due to the unification of the fundamental interactions. We evidently cannot to achieve this goal now. Together with this there are divergences in problems where the high-energy processes simply cannot be involved (say electron self-energy, Lamb's shift, etc.). Last ones reflect the formal character of perturbation theory applied to interacting secondly quantized amplitudes of the pointwise particles. These difficulties are borrowed partly from the classical theory. I would like to establish some general framework for the future unified theory avoiding to use the method of classical analogy.