The anyon model: an example inspired by string theory

TL;DR

This paper explores a novel string model inspired by string theory, constructing and quantizing a new dynamical system in 2+1 dimensions, revealing an energy spectrum with arbitrary spin and specific spectral properties.

Contribution

It introduces a new class of open finite strings in 2+1D, constructs their dynamical system, and derives an explicit energy spectrum formula with spectral problem insights.

Findings

Energy spectrum formula ${ m S} = eta_n { m E} + c_n$ established.

Arbitrary spin values are possible within the model.

Spectral properties linked to fermionic Fock space eigenvalues.

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.