A Lagrangian for the Fine-Structure Constant
Year: 2026
Type: article
Abstract: Tensor network formulation of the Lagrangian for the fine-structure constant α.The oscillating circle of radius R = π is represented as a circular MatrixProduct State (MPS) with bond dimension D = 45, where the bounded continuedfraction quotients q_i ≤ 45 play the role of virtual bonds. We prove that the generator G(θ) = L_geo(θ) I_D + ε K satisfies[G(θ_A), G(θ_B)] = 0 for all θ_A, θ_B. Hence the product of local transfermatrices collapses exactly into the exponential of the sum, with noBaker-Campbell-Hausdorff approximations. For ε = 0 and L_curv = 0 (pure bare geometry), the dominant eigenvalue of thecontracted transfer matrix yields ln(λ_max) = 4π³ + π² + π with error 10⁻¹¹ atN = 10⁶ steps. The residual O(1/N²) convergence error is due solely toquadrature of the cusps in |cos θ|. The complete effective action includes the curvature correction −1/(24A(π))and the quantum expectation −⟨K⁻¹⟩/(A(π)²π²), reproducing the CODATA 2022value to 10⁻⁹. The fine-structure constant is not a free parameter; it is theon-shell action of a geometric field. Note on Computational Reproducibility and Repository Access Zenodo Repository Note: The exact numerical verification for the capillary resonance scan (discretization steps $N \in [5000, 6500]$ with step size $\Delta N = 5$) is fully open-source and computationally reproducible. The executable Python implementation validating the Polyakov--MPS duality and pinpointing the exact analytical resonance at $N = 6160$ is hosted on GitHub and can be accessed directly at: https://github.com/blamaxim-PEPS-5D/ALPHA_FANO_SERIES/blob/main/ALPHA_FANO_SERIES/ALPHA_CODE/5.1_capillary_probe_script_resonace_scanning_for_polyakov_string_MPS_duality.py Key Implementation Details: Scan Range: $N \in [5000, 6500]$, step interval = $5$. Optimal Resonance Node: $N_{\text{steps}} = 6160$. Target Agreement: Yields $S_{\alpha} = 137.035999175448$, matching CODATA 2022 ($137.035999177000$) with a relative precision of $1.13 \times 10^{-11}$ without any empirical parameter fitting or hardcoded target values.
Author: Massimiliano Blandino
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
OpenAlex ID: W7155680037
FWCI:
Cites:
Cited by:
Related to: