DERIVATION OF U(1) GAUGE  INVARIANCE  VIA LATTICE-14 TOPOLOGICAL STRESS

DERIVATION OF U(1) GAUGE INVARIANCE VIA LATTICE-14 TOPOLOGICAL STRESS | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 26 February 2026 V2 Latest version Share on DERIVATION OF U(1) GAUGE INVARIANCE VIA LATTICE-14 TOPOLOGICAL STRESS Author : Heiko Grimberg 0009-0008-9039-4176 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.177153747.74975032/v2 220 views 76 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract In the Standard Model, local gauge invariance is introduced as a mathematical requirement to preserve the Lagrangian under local phase transformations ψ(x) → e^(iθ(x))ψ(x). This necessity "forces" the introduction of the electromagnetic field A_μ. However, the physical origin of this mechanism remains obscure. The Unified Chronofractal Field (UCF) framework (k=0) provides a geometric derivation of this phenomenon. We posit that the vacuum is a discrete, 14-mode Bravais Lattice. In this "Hardware Paradigm," a local phase shift represents a physical rotation of a lattice node relative to its neighbors. This rotation induces Topological Torsion (shear stress) in the vacuum manifold. We demonstrate that the gauge field A_μ (the photon) is not an arbitrary construct, but the elastic restoration force of the lattice reacting to minimize this torsion. Furthermore, we derive the coupling strength of this reaction—the fine-structure constant—purely from the geometric rigidity of the lattice (C=108°, ν ≈ 0.618), yielding the value α⁻¹ ≈ 137.035971. Thus, light is identified as the inevitable stress-relief mechanism of a discrete geometry. In the Standard Model, local gauge invariance is introduced as a mathematical requirement to preserve the Lagrangian under local phase transformations ψ(x) → e^(iθ(x))ψ(x). This necessity "forces" the introduction of the electromagnetic field A_μ. However, the physical origin of this mechanism remains obscure. The Unified Chronofractal Field (UCF) framework (k=0) provides a geometric derivation of this phenomenon. We posit that the vacuum is a discrete, 14-mode Bravais Lattice. In this "Hardware Paradigm," a local phase shift represents a physical rotation of a lattice node relative to its neighbors. This rotation induces Topological Torsion (shear stress) in the vacuum manifold. We demonstrate that the gauge field A_μ (the photon) is not an arbitrary construct, but the elastic restoration force of the lattice reacting to minimize this torsion. Furthermore, we derive the coupling strength of this reaction—the fine-structure constant—purely from the geometric rigidity of the lattice (C=108°, ν ≈ 0.618), yielding the value α⁻¹ ≈ 137.035971. Thus, light is identified as the inevitable stress-relief mechanism of a discrete geometry. Supplementary Material File (25_v2_derivation_of_u_1__gauge_invariance_via_lattice_14_topological_stress.pdf) Download 260.84 KB Information & Authors Information Version history V1 Version 1 19 February 2026 V2 Version 2 26 February 2026 Copyright This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License Keywords fine-structure constant gauge invariance lattice-14 quantum electrodynamics supersolidity theoretical physics topological stress u(1) symmetry unified chronofractal field Authors Affiliations Heiko Grimberg 0009-0008-9039-4176 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 220 views 76 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Heiko Grimberg. DERIVATION OF U(1) GAUGE INVARIANCE VIA LATTICE-14 TOPOLOGICAL STRESS. Authorea . 26 February 2026. DOI: https://doi.org/10.22541/au.177153747.74975032/v2 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . Format Please select one from the list RIS (ProCite, Reference Manager) EndNote BibTex Medlars RefWorks Direct import Tips for downloading citations document.getElementById('citMgrHelpLink').addEventListener('click', function() { popupHelp(this.href); return false; }); $(".js__slcInclude").on("change", function(e){ if ($(this).val() == 'refworks') $('#direct').prop("checked", false); $('#direct').prop("disabled", ($(this).val() == 'refworks')); }); View Options View options PDF View PDF Figures Tables Media Share Share Share article link Copy Link Copied! Copying failed. 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