Wedge Local Deformations of Charged Fields leading to Anyonic Commutation Relations

TL;DR

This paper generalizes a deformation method for free fields to charged fields in Minkowski space, producing anyonic commutation relations and wedge localization, thus enabling free anyons despite existing no-go theorems.

Contribution

It introduces a deformation approach for charged free fields that yields anyonic behavior and wedge localization, circumventing previous no-go theorems.

Findings

Deformed fields satisfy generalized anyonic commutation relations.

Fields are polarization free and localized in wedges.

Two-particle scattering matrix is non-trivial.

Abstract

The method of deforming free fields by using multiplication operators on Fock space, introduced by G. Lechner in [11], is generalized to a charged free field on two- and three-dimensional Minkowski space. In this case the deformation function can be chosen in such a way that the deformed fields satisfy generalized commutation relations, i.e. they behave like Anyons instead of Bosons. The fields are "polarization free" in the sense that they create only one-particle states from the vacuum and they are localized in wedges (or "paths of wedges"), which makes it possible to circumvent a No-Go theorem by J. Mund [12], stating that there are no free Anyons localized in spacelike cones. The two-particle scattering matrix, however, can be defined and is different from unity.