Bose-Fermi Transformation In Three Dimensional Space
Luis Huerta, Jorge Zanelli
TL;DR
This paper generalizes the Jordan-Wigner transformation to three dimensions, mapping spin systems to fermionic theories coupled with nonabelian gauge fields and monopoles, revealing new topological and gauge structures.
Contribution
It introduces a novel three-dimensional Jordan-Wigner transformation expressed as a gauge transformation with topological charge one.
Findings
Fermionic theory minimally coupled to nonabelian gauge fields
Topological charge of the gauge transformation is one
Inclusion of monopoles in the gauge field structure
Abstract
A generalization of the Jordan-Wigner transformation to three (or higher) dimensions is constructed. The nonlocal mapping of spin to fermionic variables is expressed as a gauge transformation with topological charge equal to one. The resulting fermionic theory is minimally coupled to a nonabelian gauge field in a spontaneously broken phase containing monopoles.
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