On the connetion between Euclidean and Hamiltonian lattice field theories of vortices and anyons

In the (2+1)-dimensional non-compact Abelian lattice Higgs model Euclidean correlation functions of vortices and, after adding the Chern-Simons term to the action, correlation functions of transmuted matter fields (anyons) are set up. These correlation functions satisfy Osterwalder-Schrader positivity. Via the transition to continuous Euclidean time, vortex and anyon operators within a Hamiltonian lattice formulation are obtained, respectively, and their respective dual algebras are displayed.