Aplicación del F α -Cálculo a la Anomalía Magnética del Electrón: Una Derivación Topológica de los Coeficientes QED y el problema de la Jerarquía. / Application of F α -Calculus to the Anomalous Magnetic Moment of the Electron: A Topological Derivation of QED Coefficients and the Hierarchy Problem
Authors/Creators
Description
Proponemos que la divergencia asintótica de la QED surge de la topología fractal del vacío. Aplicando el formalismo del F α -Calculus al momento magnético del electrón, identificamos una dimensión efectiva µ ≈ 0,757. Este marco geométrico unifica la constante de estructura fina (α) y la constante de gravitación (G) interpretando la masa como fricción topológica. El modelo ofrece una predicción falsable: C6 ≈ −20,26.
- Incluye preprint - nueva version reducida -
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We propose that the asymptotic divergence of QED arises from the fractal topology of the vacuum. By applying the F α -Calculus formalism to the anomalous magnetic moment of the electron, we identify an effective dimension µ ≈ 0.757. This geometric framework unifies the fine-structure constant (α) and the universal gravitational constant (G) by interpreting mass as topological friction. The model offers a falsifiable prediction: C6 ≈ −20.26.
- inclues preprint - new reduced version -
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Fa_Calculus_TEU__GITHUB.pdf
Additional details
Related works
- Is supplemented by
- Computational notebook: https://github.com/marianomarincasado-ux/TEU-Fa-Calculus-QED-G (URL)
Software
- Repository URL
- https://github.com/marianomarincasado-ux/TEU-Fa-Calculus-QED-G.git
- Programming language
- Python
References
- Lygeros, N. (1994). Fractals et posets en relativité. Annales de la Fondation Louis de Broglie, Vol. 19, No. 4. https://fondationlouisdebroglie.org/AFLB-194/LYGEROS. TEX2.pdf
- L. F. Abbott and M. B. Wise, Dimension of a quantum path, Am. J. Phys. 49, 37 (1981). DOI: 10.1119/1.12657.
- L. Nottale, Scale relativity and fractal space-time: Application to quantum physics, cosmology and chaotic systems, Chaos, Solitons & Fractals 7, 877–938 (1996).
- A. Deppman, E. Megías, and R. Pasechnik, Fractal derivatives, fractional derivatives and q-deformed calculus, Entropy 25, 1008 (2023); arXiv:2305.04633 [math-ph].
- A. Parvate, A. D. Gangal. Calculus on Fractal Curves in R n . Fractals, Vol. 17, No. 01, pp. 53-81 (2009).
- S. Satin, A. D. Gangal. Random Walk and Broad Distributions on Fractal Curves. arXiv:1103.5249 [math-ph] (2011).
- Gianluca Calcagni. Geometry and field theory in multi-fractional spacetime JHEP01(2012)065 / arXiv:1107.5041 https://doi.org/10.48550/arXiv.1107.5041
- T. Aoyama, M. Hayakawa, A. Hirayama, M. Nio Verification of the tenth-Order QED contribution to the anomalous magnetic moment of the electron from diagrams without fermion loops /arXiv:2412.06473 https://doi.org/10.48550/arXiv.2412.06473
- N. Laskin. Fractional Schrodinger equation. Phys,Rev,E66:056108,2002. https:// arxiv.org/abs/quant-ph/0206098
- R. Metzler, J. Klafter. The random walk's guide to anomalous diffusion: a fractional dynamics approach. Phys Rep Phys Rep. Physics Reports. 339. 10.1016/s0370-15730000070- 3.
- L. Nottale, "Scale Relativity, Fractal Space-Time and Quantum Mechanics", Chaos, Solitons & Fractals 4, 361–426 (1994)
- L. Nottale, "The Theory of Scale Relativity: Non-Differentiable Geometry and Fractal Space-Time", AIP Conf. Proc. 718, 68–95 (2004). https://doi.org/10.1063/1. 1787313
- T. Aoyama, T. Kinoshita, M. Nio. Revised and Improved Value of the QED Tenth-Order Electron Anomalous Magnetic Moment. Atoms 7(1), 28 (2019)
- S. Volkov, Calculation of the total 10th order QED contribution to the electron magnetic moment, Phys. Rev. D 110, 036001 (2024).
- T. Aoyama, M. Hayakawa, A. Hirayama, and M. Nio, Verification of the tenth-order QED contribution to the anomalous magnetic moment of the electron from diagrams without fermion loops, arXiv:2412.06473 [hep-ph] (2024).
- A. K. Golmankhaneh and D. Baleanu, Schrödinger Equation on Fractals Curves Imbedding in R3 , arXiv:1308.0291 [math-ph] (2013).
- X. Fan et al. Measurement of the Electron Magnetic Moment. Phys. Rev. Lett. 130, 071801 (2023).
- F. J. Dyson. Divergence of perturbation theory in quantum electrodynamics. Phys. Rev. 85, 631 (1952).
- R. Penrose, On the Nature of Quantum Geometry, in Magic Without Magic: John Archibald Wheeler, ed. J. Klauder (W. H. Freeman, San Francisco, 1972), pp. 333–354.
- A. D. Sakharov, Vacuum quantum fluctuations in curved space and the theory of gravitation, Gen. Relativ. Gravit. 32, 365–367 (2000) [Reprinted from Dokl. Akad. Nauk SSSR 177, 70 (1967)].
- L. Giani and O. F. Piattella, Induced non-local cosmology, Phys. Dark Univ. 42, 101270 (2023); arXiv:2302.06762 [gr-qc]. https://doi.org/10.48550/arXiv.2302.06762
- M. Visser, Sakharov's induced gravity: a modern perspective, Mod. Phys. Lett. A 17, 977–992 (2002); arXiv:gr-qc/0204062. https://arxiv.org/pdf/gr-qc/0204062
- F. Sun and J. Ye, Two classes of organization principle: quantum/topological phase transitions meet complete/in-complete devil staircases, arXiv:1603.00451 [cond-mat.strel] (2016).
- T. Aoyama, T. Kinoshita, M. Nio, Phys. Rev. D 97, 036001 (2018).
- S. Laporta, High-precision calculation of the 4-loop contribution to the electron g-2, INFN Presentation (2017).