The anyon model: an example inspired by string theory

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 $\mathsf{S}={\alpha }_n\mathsf{E}+c_n$; the spin $\mathsf{S}$ is an arbitrary number here but the constants ${\alpha }_n$ and $c_n$ are eigenvalues for certain spectral problems in fermionic Fock space ${\mathbf{H}}_{\psi }$ constructed for the free 2D fermionic field.