Quantum field theories of vortices and anyons.

We develop the quantization of topological solitons (vortices) in three-dimensional quantum field theory, in terms of the Euclidean region functional integral. We analyze in some detail the vortices of the abelian Higgs model. If a Chern-Simons term is added to the action, the vortices turn out to be ldquoanyons,rdquo i.e. particles with arbitrary real spin and intermediate (THgr) statistics. Localization properties of the interpolating field, scattering theory and spin-statistics connection of anyons are discussed. Such analysis might be relevant in connection with the fractional quantum Hall effect and two-dimensional models of HighT csuperconductors.