Heisenberg's S-matrix program and Feynman's divergence problem
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911317998174208 |
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| author | Sakhnovich, Lev |
| author_facet | Sakhnovich, Lev |
| contents | 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 $\varepsilon$ and carried out rigorously?" |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_02847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Heisenberg's S-matrix program and Feynman's divergence problem Sakhnovich, Lev Mathematical Physics High Energy Physics - Theory Spectral Theory Quantum Physics 81T15, 34L25, 81Q05, 81Q30 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 $\varepsilon$ and carried out rigorously?" |
| title | Heisenberg's S-matrix program and Feynman's divergence problem |
| topic | Mathematical Physics High Energy Physics - Theory Spectral Theory Quantum Physics 81T15, 34L25, 81Q05, 81Q30 |
| url | https://arxiv.org/abs/2511.02847 |