Topological Fermions from Framed Vortex Loops in a Quantized Superfluid Effective Field Theory (v7) Part I
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| Format: | Recurso digital |
| Sprache: | Englisch |
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2026
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| _version_ | 1866901146004619264 |
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| author | Smith, Alex |
| author_facet | Smith, Alex |
| contents | <p>We present an emergent hydrodynamic framework for fermionic statistics within a 3 + 1-dimensional quantized superfluid effective field theory (EFT). While classi-<br>cal vortices in irrotational fluids are bosonic, we demonstrate that quantized vortex loops generically acquire an effective internal framing arising from the anisotropic<br>geometry and phase-gradient structure of their cores. These framed vortex loops inhabit a configuration space C ∼= (T 3 × SO(3))N /SN . We define the Berry con-<br>nection on the Hilbert bundle of condensate states and show that the adiabatic exchange of two such defects corresponds to a non-contractible loop in SO(3). Due<br>to π1(SO(3)) ∼= Z2, the resulting holonomy yields a topological phase π, producing the fermionic exchange sign eiπ = −1. This provides a concrete mechanical real-<br>ization of the Finkelstein–Rubinstein constraint and demonstrates the possibility that half-integer spin and fermionic exchange statistics can emerge as topological<br>properties of a superfluid vacuum.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18563180 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Topological Fermions from Framed Vortex Loops in a Quantized Superfluid Effective Field Theory (v7) Part I Smith, Alex emergent quantum field theory topological solitons fermionic statistics Abelian statistics superfluid vacuum Berry phase Finkelstein-Rubinstein constraint vortex dynamics spin-statistics connection effective field theory topological defects SO(3) topology <p>We present an emergent hydrodynamic framework for fermionic statistics within a 3 + 1-dimensional quantized superfluid effective field theory (EFT). While classi-<br>cal vortices in irrotational fluids are bosonic, we demonstrate that quantized vortex loops generically acquire an effective internal framing arising from the anisotropic<br>geometry and phase-gradient structure of their cores. These framed vortex loops inhabit a configuration space C ∼= (T 3 × SO(3))N /SN . We define the Berry con-<br>nection on the Hilbert bundle of condensate states and show that the adiabatic exchange of two such defects corresponds to a non-contractible loop in SO(3). Due<br>to π1(SO(3)) ∼= Z2, the resulting holonomy yields a topological phase π, producing the fermionic exchange sign eiπ = −1. This provides a concrete mechanical real-<br>ization of the Finkelstein–Rubinstein constraint and demonstrates the possibility that half-integer spin and fermionic exchange statistics can emerge as topological<br>properties of a superfluid vacuum.</p> |
| title | Topological Fermions from Framed Vortex Loops in a Quantized Superfluid Effective Field Theory (v7) Part I |
| topic | emergent quantum field theory topological solitons fermionic statistics Abelian statistics superfluid vacuum Berry phase Finkelstein-Rubinstein constraint vortex dynamics spin-statistics connection effective field theory topological defects SO(3) topology |
| url | https://doi.org/10.5281/zenodo.18563180 |