Derivation of the Fine Structure Constant from a Scalar Field Theory on a φ-Metric 7-Torus
Year: 2026
Type: preprint
Abstract: We present a candidate derivation of the electromagnetic fine structure constant α from a nonlinear scalar field equation on an 8-dimensional compact manifold. The field is octonionic-valued, and the manifold is T⁷ × S¹ equipped with a metric whose compact radii scale as successive inverse powers of the golden ratio φ = (1+√5)/2. The equation □_φΨ + (|Ψ|²−φ)Ψ = 0 admits topological soliton solutions whose quantum fluctuations induce a non-perturbative vacuum displacement κ₀. We identify specific geometric mechanisms — G₂-structure calibrations on the octonionic tangent bundle and Kaluza–Klein charge summation — that motivate the tree-level and one-loop contributions. The G₂-structure calibration contributing a factor (2π)² to the tree-level coupling is corroborated by a lower-dimensional SU(3)-structure analogue on T⁶ (Appendix C); explicit Kaluza–Klein reduction on the octonionic T⁷ remains the primary open verification requirement. The resulting formula, 1/α = (2π)¹⁰/φ²⁸ + (49/32π²)ln(φ²⁸/ln2), contains no free parameters and yields 1/α = 137.088576695, within 0.038% of the CODATA 2022 experimental value 137.035 999 177(21). We analyse the residual discrepancy as a higher-order effect, identifying the Casimir correction to the tree-level volume as the primary candidate with confirmed correct sign.
Author: Mudway, Lee
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7141276711
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