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Geometric Model of Fermions and the Fine-Structure Constant

Sabir S. Asadullaev

A novel geometric model is proposed, in which fundamental fermions are represented as stable configurations of three mutually orthogonal vortices in the form of Möbius strips. From the geometry of the model, it is derived that the minimal size of a fermion is bounded from below by a radius of R_f = 2(2+sqrt(3))/3 ≈ 2.488 Planck lengths L_p. It is shown that the total geometrized path of the configuration over a fundamental cycle, normalized to L_p, yields a value for the inverse fine-structure constant 1/α = 6sqrt(3)(9+4pi/3) ≈ 137.062, which coincides with the experimental value to an accuracy of 0.02%. In addition, the construction of the model naturally allows for the existence of electric charges quantized in units of e/3, which is qualitatively consistent with the charge spectrum of quarks and leptons in the Standard Model.