English

Heisenberg's S-matrix program and Feynman's divergence problem

Mathematical Physics 2025-12-16 v2 High Energy Physics - Theory math.MP Spectral Theory Quantum Physics

Abstract

In the present article, we assume that the first approximation of the scattering operator is given and that it has the logarithmic divergence. This first approximation allows us to construct the so called deviation factor. Using the deviation factor, we regularize all terms of the scattering operator's approximations. The infrared and ultraviolet cases as well as concrete examples are considered. Thus, for a wide range of cases, we provide a positive answer to the well-known problem of J. R. Oppenheimer regarding scattering operators in QED: ``Can the procedure be freed of the expansion in ε\varepsilon and carried out rigorously?"

Keywords

Cite

@article{arxiv.2511.02847,
  title  = {Heisenberg's S-matrix program and Feynman's divergence problem},
  author = {Lev Sakhnovich},
  journal= {arXiv preprint arXiv:2511.02847},
  year   = {2025}
}

Comments

This work is an important development of our manuscripts arXiv:1602.07087 and arXiv:1710.08363. In the second version of this work some corrections and simplifications are made

R2 v1 2026-07-01T07:21:47.058Z