Letters in Mathematical Physics

, Volume 105, Issue 8, pp 1033–1055 | Cite as

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

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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 S1 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.

Mathematics Subject Classification

81T05 81T10 81T40 20F36 22E67 

Keywords

quantum field theory braid group statistics anyons implementable Bogoliubov transformations 

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Faculty of PhysicsUniversity of ViennaViennaAustria

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