V64: Renormalization without Renormalization — Recovery of Natural Finiteness via the Dynamic Space Function Σ
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2026
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| _version_ | 1866901140895956992 |
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| author | Yoshida, Satoshi ChatGPT, A. Gemini, G. Claude, C. |
| author_facet | Yoshida, Satoshi ChatGPT, A. Gemini, G. Claude, C. |
| contents | <p>Renormalization has long been regarded as an unavoidable but conceptually unsatisfactory procedure in quantum field theory, required to cancel divergent quantities arising from point-particle assumptions in a static vacuum. In this work, we demonstrate that these divergences are not fundamental, but rather artifacts of assuming a static background space. By introducing the space function Σ, originally developed in V60 as a dynamically generated spatial resolution, we show that self-energy terms become finite without subtraction or redefinition. Numerical simulations confirm smooth convergence of electron self-energy and reveal a universal invariant linking particle mass and spatial structure. Renormalization is thus reinterpreted as an emergent approximation of a deeper update-continuity principle. The Ward–Takahashi identity is preserved under Σ-regularization, demonstrating that gauge invariance and Lorentz covariance are maintained.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18144047 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | V64: Renormalization without Renormalization — Recovery of Natural Finiteness via the Dynamic Space Function Σ Yoshida, Satoshi ChatGPT, A. Gemini, G. Claude, C. renormalization, quantum field theory, dynamic space function, Σ-regularization, UV finiteness, self-energy, Ward-Takahashi identity, gauge invariance, update continuity, YAGC <p>Renormalization has long been regarded as an unavoidable but conceptually unsatisfactory procedure in quantum field theory, required to cancel divergent quantities arising from point-particle assumptions in a static vacuum. In this work, we demonstrate that these divergences are not fundamental, but rather artifacts of assuming a static background space. By introducing the space function Σ, originally developed in V60 as a dynamically generated spatial resolution, we show that self-energy terms become finite without subtraction or redefinition. Numerical simulations confirm smooth convergence of electron self-energy and reveal a universal invariant linking particle mass and spatial structure. Renormalization is thus reinterpreted as an emergent approximation of a deeper update-continuity principle. The Ward–Takahashi identity is preserved under Σ-regularization, demonstrating that gauge invariance and Lorentz covariance are maintained.</p> |
| title | V64: Renormalization without Renormalization — Recovery of Natural Finiteness via the Dynamic Space Function Σ |
| topic | renormalization, quantum field theory, dynamic space function, Σ-regularization, UV finiteness, self-energy, Ward-Takahashi identity, gauge invariance, update continuity, YAGC |
| url | https://doi.org/10.5281/zenodo.18144047 |