Local Anyonic Quantum Fields on the Circle Leading to Cone-Local Anyons in Two Dimensions

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.