The anyon model: an example inspired by string theory

Abstract

We investigate the enlarged class of open finite strings in $(2+1)D$ space-time. The new dynamical system related to this class is constructed and quantized here. As the result, the energy spectrum of the model is defined by a simple formula ${\sf S} = \alpha_n{\sf E} + c_n$; the spin ${\sf S}$ is an arbitrary number here but the constants $\alpha_n$ and $c_n$ are eigenvalues for certain spectral problems in fermionic Fock space ${\bf H}_\psi$ constructed for the free 2D fermionic field.