# Local Quantum Fields for Anyons on the Circle leading to Non-Relativistic Anyons in Two Dimensions

May 16, 2014

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 $\mathbb{R}^2$ one can obtain a
non-relativistic cone-localized field net for Anyons in two dimensions.

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