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2025
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| Online Access: | https://doi.org/10.5281/zenodo.15500220 |
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| _version_ | 1866902335622479872 |
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| author | Washburn, Jonathan |
| author_facet | Washburn, Jonathan |
| contents | <p>Motivation. Feynman diagrams distill quantum-field amplitudes into beautiful pictures--then send practitioners on a detour through ultraviolet-divergent integrals and renormalisation counter-terms.</p> <p>Idea. We replace those integrals by finite sums of closed voxel walks. Every hop carries an amplitude A_step = sqrt(P) * phi^(-1/2), where P is the field's ledger residue share and phi the golden ratio. The signed, unordered count of 2k-tick walks is the simple combinatorial law N_2k = 3 * 2^(k-1); the geometric series converges instantly.</p> <p>Results. Without regulators or tunable constants the ledger reproduces: Schwinger's electron (and muon) anomalous moment a^(1)_e,mu = 1.1608(6) x 10^(-3) (99.95% of alpha/2pi); the photon vacuum-polarisation slope Pi'(0) = 7.737(4) x 10^(-4) (99.93%); and the on-shell quark chromo-magnetic coefficient (g_s - 2)/2 = 7.574(8) x 10^(-3) (100.9% of C_F * alpha_s / 2pi). Ward-identity open walks satisfy Z_1 = Z_2 to better than 10^(-4).</p> <p>Significance. A handful of integer walks, an eight-beat phase average, and a golden-ratio weight reproduce all one-loop QED and QCD numbers--no infinities required. The method offers a finite, combinatorial alternative to perturbative integrals and a compact road map for higher-loop calculations.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15500220 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Finite Voxel-Walk Representation of One-Loop QED and QCD Amplitudes Washburn, Jonathan <p>Motivation. Feynman diagrams distill quantum-field amplitudes into beautiful pictures--then send practitioners on a detour through ultraviolet-divergent integrals and renormalisation counter-terms.</p> <p>Idea. We replace those integrals by finite sums of closed voxel walks. Every hop carries an amplitude A_step = sqrt(P) * phi^(-1/2), where P is the field's ledger residue share and phi the golden ratio. The signed, unordered count of 2k-tick walks is the simple combinatorial law N_2k = 3 * 2^(k-1); the geometric series converges instantly.</p> <p>Results. Without regulators or tunable constants the ledger reproduces: Schwinger's electron (and muon) anomalous moment a^(1)_e,mu = 1.1608(6) x 10^(-3) (99.95% of alpha/2pi); the photon vacuum-polarisation slope Pi'(0) = 7.737(4) x 10^(-4) (99.93%); and the on-shell quark chromo-magnetic coefficient (g_s - 2)/2 = 7.574(8) x 10^(-3) (100.9% of C_F * alpha_s / 2pi). Ward-identity open walks satisfy Z_1 = Z_2 to better than 10^(-4).</p> <p>Significance. A handful of integer walks, an eight-beat phase average, and a golden-ratio weight reproduce all one-loop QED and QCD numbers--no infinities required. The method offers a finite, combinatorial alternative to perturbative integrals and a compact road map for higher-loop calculations.</p> |
| title | Finite Voxel-Walk Representation of One-Loop QED and QCD Amplitudes |
| url | https://doi.org/10.5281/zenodo.15500220 |