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| Format: | Recurso digital |
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Zenodo
2025
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| Online Access: | https://doi.org/10.5281/zenodo.18051320 |
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Table of Contents:
- <p>This paper presents a comprehensive synthesis demonstrating that the complete hierarchy of gauge symmetries---U(1), SU(2), SU(3)---together with fundamental quantum phenomena including the Pauli exclusion principle and anomalous Zeeman effect, emerge necessarily from a single geometric principle: <strong>volume-preserving dynamics in the golden-rhombohedral vacuum. </strong></p> <p>We develop <strong>three complementary derivation approaches</strong> that converge on identical results: (1) a <em>topological approach</em> based on the binary icosahedral group 2I and Berry phase accumulation, (2) a <em>symmetry approach</em> based on RHC reflection symmetry and bidirectional coupling, and (3) a <em>dynamical approach</em> based on Cosserat micropolar mechanics and core-vacuum angular momentum partition. The remarkable convergence of three independent methods---algebraic/topological, geometric/symmetry, and mechanical/dynamical---provides compelling validation that we have identified fundamental organizing principles of nature.</p> <p>The vacuum is modeled as a Cosserat-elastic quasicrystal with discrete cell size <em>L</em>cell = 0.3815 fm, composed of acute and obtuse golden rhombohedra with icosahedral ($A_5$) symmetry. We prove that: (i) the fine-structure constant $\alpha$ arises from U(1) phase evolution constrained by Cosserat closure at $t_1 + t_2 = 1 - \alpha^2$; (ii) fermionic statistics and $g_s = 2$ emerge from SU(2) spinor structure through three independent mechanisms; (iii) SU(3) color symmetry follows necessarily from volume-preserving three-channel scattering, where the traceless constraint Tr[<em>H</em>] = 0 preventing ``gimbal lock'' forces $\det M = 1$.</p> <p>We establish that these apparently different constraints are mathematically equivalent expressions of a single master principle: <em>global phase (U(1)) factorizes from volume-preserving rotational mixing (SU($N$)) in a structured Cosserat medium</em>. The confinement scale of QCD ($\sim$1 fm) coincides with the vacuum cell hierarchy, suggesting color charge is a geometric property of wave propagation through structured three-dimensional space. This framework replaces the Standard Model's postulated gauge groups with geometric necessities, offering new perspectives on grand unification and the origin of fundamental constants.</p> <p>The paper is structured as an interdisciplinary teaching document, presenting detailed derivations accessible to researchers in theoretical physics, mathematical physics, and condensed matter theory, while maintaining rigorous mathematical foundations throughout.</p>