Quantization of solitons in terms of Euclidean region functional integrals is developed, and Osterwalder-Schrader reconstruction is extended to theories with topological solitons. The quantization method is applied to several lattice field theories with solitons, and the particle structure in the soliton sectors of such theories is analyzed. A construction of magnetic monopoles in the fourdimensional, compact t/(l)-model, in the QED phase, is indicated as well.

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 "anyons," i.e. particles with arbitrary real spin and intermediate (Θ) 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 twodimensional models of High T c superconductors.

Abstract. We present a general method to bosonize systems of Fermions with innitely many degrees of freedom, in particular systems of non-relativistic electrons at positive density, b y expressing the quantized conserved electric chargeand current density in terms of a bosonic antisymmetric tensoreld of a rank d{1, where d is the dimension of space. This enables us to make concepts and tools from gauge theory available for the purpose of analyzing electronic structure of non-relativistic matter. We apply our bosonization identities and concepts from gauge theory, such a s W egner -'t Hooft duality, t o a v ariety of systems of condensed matter physics: Landau-Fermi liquids, Hall uids, London superconductors, etc.. Among our results are an exact formula for the plasmon gap in a metal, a simple derivation of the Anderson-Higgs mechanism in superconductors, and an analysis of the orthogonality catastrophe for static sources.