Abstract
Using the method of implementable one-particle Bogoliubov transformations, it is possible to explicitly define a local covariant net of quantum fields on the (universal covering of the) circle S 1 with braid group statistics. These anyon fields transform under a representation of \({\widetilde{U(1)}}\) for arbitrary real-valued spin and their commutation relations depend on the relative winding number of localization regions. By taking the tensor product with a local covariant field theory on \({{{\rm{I\!R}}}^2}\), one can obtain a (non-boost covariant) cone-localized field net for anyons in two dimensions.
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Plaschke, M. Local Anyonic Quantum Fields on the Circle Leading to Cone-Local Anyons in Two Dimensions. Lett Math Phys 105, 1033–1055 (2015). https://doi.org/10.1007/s11005-015-0767-9
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DOI: https://doi.org/10.1007/s11005-015-0767-9