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arXiv · 1405.4154

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

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

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Matthias Plaschke. 2015-01-15. Local Quantum Fields for Anyons on the Circle leading to Non-Relativistic Anyons in Two Dimensions. https://doi.org/10.1007/s11005-015-0767-9

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