2025/10/24 by Lev Sakhnovich, Sakhnovich, Lev
Mathematics · #34L25 #81Q05 #81Q30 #81T15 #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2511.02847
openalex publication_date 2025/10/24 · openalex created_date 2025/11/07 · openalex updated_date 2026/07/28
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 and carried out rigorously?"