SCATTERING PROPERTIES OF ANYONS AND PLEKTONS

The present knowledge about scattering theory of abelian and nonabelian braid-group statistics particles is reviewed. Recent developments are analyzed in the light of (often apparently unnoticed) older observations. One characteristic property of the S-matrix is its factorization into a nonanalytic "kinematical" part and a "dynamical" analytic part where the latter complies with analytic properties well-known from permutation group statistics dispersion relations. For the kinematical part we write down an explicit formula in terms of braid group data. This formula is consistent with the known lack of manifest Lorentz covariances of scattering states resulting from the presence of a "spectator string". We comment on the relation of this piecewise constant S-matrix to the Leinhaas-Myrheim geometric picture and to the possible existence of localized free anyon and plekton fields. At the end we present some open problems which stand between the known results and potential applications to low-dimensional physics.