Anyons as spin particles: from classical mechanics to field theory

TL;DR

This paper explores (2+1)-dimensional relativistic fractional spin particles, known as anyons, using a group-theoretical approach from classical mechanics to field theory, establishing foundational equations.

Contribution

It develops a comprehensive framework connecting classical mechanics and field theory for anyons with fractional spin, providing minimal linear differential equations.

Findings

Derived minimal set of linear differential field equations for anyons.

Unified classical and field theoretical description of fractional spin particles.

Enhanced understanding of the group-theoretical structure of anyons.

Abstract

(2+1)-dimensional relativistic fractional spin particles are considered within the framework of the group-theoretical approach to anyons starting from the level of classical mechanics and concluding by the construction of the minimal set of linear differential field equations.