Paper XXXVII: Topological Origin of Spin and the Spin-Statistics Connection
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2026
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| _version_ | 1866901793282195456 |
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| author | Novickis, Alexander |
| author_facet | Novickis, Alexander |
| contents | <div> <h4>Abstract</h4> <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> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>spin</span> <span>statistics</span> <span>fermion</span> <span>boson</span> <span>topology</span> <span>soliton</span> <span>hopf</span> <span>finkelstein rubinstein</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-03-26</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19163319">10.5281/zenodo.19163319</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
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| spellingShingle | Paper XXXVII: Topological Origin of Spin and the Spin-Statistics Connection Novickis, Alexander 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 physics spin statistics fermion boson topology soliton hopf finkelstein-rubinstein <div> <h4>Abstract</h4> <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> </div> <h3>Keywords</h3> <div> <span>physics</span> <span>spin</span> <span>statistics</span> <span>fermion</span> <span>boson</span> <span>topology</span> <span>soliton</span> <span>hopf</span> <span>finkelstein rubinstein</span> </div> <div> <div> <div>Type</div> <div>Preprint</div> </div> <div> <div>License</div> <div>CC BY 4.0</div> </div> <div> <div>Date</div> <div>2026-03-26</div> </div> <div> <div>Subject</div> <div>Theoretical Physics</div> </div> <div> <div>DOI</div> <div><a href="https://doi.org/10.5281/zenodo.19163319">10.5281/zenodo.19163319</a></div> </div> </div> <div> © 2026 Alexander Novickis. Licensed under <a href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International</a>. </div> |
| title | Paper XXXVII: Topological Origin of Spin and the Spin-Statistics Connection |
| topic | 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 physics spin statistics fermion boson topology soliton hopf finkelstein-rubinstein |
| url | https://doi.org/10.5281/zenodo.19294980 |