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| Format: | Recurso digital |
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Zenodo
2026
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| Accès en ligne: | https://doi.org/10.5281/zenodo.19625893 |
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- <p><strong>Title:</strong> Paper XXXVII: Topological Origin of Spin and the Spin-Statistics Connection</p> <p><strong>Author:</strong> Alexander Novickis (alex.novickis@gmail.com)</p> <p>We demonstrate that the spin-statistics connection -- fermions carry half-integer spin and obey Fermi-Dirac statistics, bosons carry integer spin and obey Bose-Einstein statistics -- emerges as a topological theorem within the Hopf soliton framework, requiring no independent axiom. The configuration space of a single Hopf soliton with charge $H \neq 0$ is the mapping space $\mathcal{Q} = \text{Maps}_H(S^3, S^2)$, whose fundamental group $\pi_1(\mathcal{Q}) = \mathbb{Z}_2$ renders $2\pi$ rotation topologically non-trivial. The Finkelstein-Rubinstein construction then selects the double-valued (fermionic) quantization: wavefunctions on $\mathcal{Q}$ acquire a sign under $2\pi$ rotation, yielding spin-1/2. Exchange of two identical $H \neq 0$ solitons is topologically equivalent to $2\pi$ rotation of one, enforcing antisymmetric wavefunctions -- the Pauli exclusion principle derived from topology. The photon ($H=0$) has simply connected configuration space ($\pi_1 = 0$), automatically giving integer spin and Bose-Einstein statistics. In 2+1 dimensions, the fundamental group becomes $\mathbb{Z}$ (the braid group), producing anyonic statistics. The geometric (Berry) phase under adiabatic rotation reproduces the FR sign rule exactly. We compare this topological proof with the Streater-Wightman axiomatic proof and identify the structural reasons for their agreement.</p> <p><b>Keywords:</b> spin-statistics theorem, Finkelstein-Rubinstein quantization, Hopf soliton, configuration space topology, fundamental group, Pauli exclusion principle, anyons, Berry phase, braid group, topological quantum field theory</p> <p><strong>Keywords:</strong> physics, spin, statistics, fermion, boson, topology, soliton, hopf, finkelstein rubinstein</p> <p><strong>DOI:</strong> <a href="https://doi.org/10.5281/zenodo.19349049">10.5281/zenodo.19349049</a></p> <p><strong>Series:</strong> Paper XXXVII in the Hopf Soliton Programme</p>