An anyon model

We construct an infinite-dimensional dynamical Hamiltonian system that can be interpreted as a localized structure (“quasiparticle”) on the plane $E_{2}$. The model is based on the theory of an infinite string in the Minkowski space $E_{1,3}$ formulated in terms of the second fundamental forms of the worldsheet. The model phase space $\mathcal H$ is parameterized by the coordinates, which are interpreted as “internal” ($E(2)$-invariant) and “external” (elements of $T^*E_{2}$) degrees of freedom. The construction is nontrivial because $\mathcal H$ contains a finite number of constraints entangling these two groups of coordinates. We obtain the expressions for the energy and for the effective mass of the constructed system and the formula relating the proper angular momentum and the energy. We consider a possible interpretation of the proposed construction as an anyon model.