A Hypercomplex Fiber Model of the Electron: Geometry, Spin, and Transient Structure Beyond Complex Quantum States

A Hypercomplex Fiber Model of the Electron: Geometry, Spin, and Transient Structure Beyond Complex Quantum States | 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 Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed.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. 21 January 2026 V1 Latest version Share on A Hypercomplex Fiber Model of the Electron: Geometry, Spin, and Transient Structure Beyond Complex Quantum States Author : Abhishek Bansal 0000-0002-2572-9004 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.176901791.19285874/v1 101 views 53 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract The conventional quantum-mechanical description of the electron represents physical states as complexvalued wavefunctions evolving in a Hilbert space over C. While empirically successful, this formulation incorporates several essential features of the electron-such as spin, orbital geometry, geometric phase, tunneling, chirality, and transient internal structure-only indirectly, through auxiliary formalisms or externally imposed symmetries, rather than as intrinsic components of the quantum state itself. In this work, we propose a hypercomplex fiber model of the electron within a unified geometricalgebraic framework consisting of the Bansal Manifold, Bansal Space, and Bansal Algebra. Quantum states are formulated as algebra-valued fields defined over a contextual base manifold, with observable physics arising through admissible projection onto associative subalgebras. The internal fiber algebra extends beyond C to include real, complex, split-complex, quaternionic, split-quaternionic, octonionic, dual-quaternionic, dual-octonionic, and nilpotent sectors, organized into a strict hierarchy governed by associativity and projection admissibility. Within this stratified structure, the electron is modeled as a layered entity in which charge, phase, spin, orbital geometry, and transient substructure occupy distinct algebraic strata. Non-associative components do not admit direct projection into observables, providing a natural algebraic mechanism for confinement-like behavior, while nilpotent extensions encode tunneling and threshold-activated phenomena without modifying leading-order spectral predictions. An algebra-valued Schrödinger equation is formulated on the Bansal Space, whose complex projection reproduces the standard Schrödinger dynamics exactly. The framework further admits a structured SU(10) action as an internal automorphism symmetry of the hypercomplex fiber, unifying spinorial, geometric, and subatomic degrees of freedom. Familiar Standard Model symmetries arise as projection-level residues, without introducing new particles, forces, or violations of established physical laws. Complex quantum mechanics thus emerges as a stable and observable projection of a richer underlying algebraic geometry, providing a controlled and testable extension of the electron's theoretical description. Supplementary Material File (abhishekbansal_model_type2.pdf) Download 417.77 KB Information & Authors Information Version history V1 Version 1 21 January 2026 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords algebra-valued wavefunction electron structure geometric phase hypercomplex algebra internal symmetry projection admissibility quantum mechanics quaternionic and octonionic structures su(10) tunneling dynamics Authors Affiliations Abhishek Bansal 0000-0002-2572-9004 [email protected] New Era Consultancy Services View all articles by this author Metrics & Citations Metrics Article Usage 101 views 53 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Abhishek Bansal. A Hypercomplex Fiber Model of the Electron: Geometry, Spin, and Transient Structure Beyond Complex Quantum States. Authorea . 21 January 2026. DOI: https://doi.org/10.22541/au.176901791.19285874/v1 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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