Local Quantum Fields for Anyons on the Circle leading to Non-Relativistic 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 ${\mathbb{R}}^2$ one can obtain a non-relativistic cone-localized field net for Anyons in two dimensions.

References in corpus (5)

• Hardy and Lieb-Thirring inequalities for anyons
• Local exclusion and Lieb-Thirring inequalities for intermediate and fractional statistics
• The Spin-Statistics Theorem for Anyons and Plektons in d=2+1
• Braid group statistics implies scattering in three-dimensional local quantum physics
• Wedge Local Deformations of Charged Fields leading to Anyonic Commutation Relations