Wedge Local Deformations of Charged Fields leading to Anyonic Commutation Relations
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.
Keywords
Cite
@article{arxiv.1208.6141,
title = {Wedge Local Deformations of Charged Fields leading to Anyonic Commutation Relations},
author = {Matthias Plaschke},
journal= {arXiv preprint arXiv:1208.6141},
year = {2015}
}