On the Geometry of Relativistic Anyon

TL;DR

This paper introduces a twistor-based model for free relativistic anyons, revealing their geometric structure and quantum mechanics through Hamiltonian reduction and group representations.

Contribution

It presents a novel twistor model for relativistic anyons and analyzes their phase space and quantum mechanics using Hamiltonian reduction and Poincare group representations.

Findings

Phase space is a cotangent bundle of the Lobachevsky plane with a twisted symplectic structure.

Quantum states correspond to irreducible representations of the (2+1)-dimensional Poincare group.

Hamiltonian reduction yields minimal covariant and anyon models with specific geometric and algebraic properties.

Abstract

A twistor model is proposed for the free relativistic anyon. The Hamiltonian reduction of this model by the action of the spin generator leads to the minimal covariant model; whereas that by the action of spin and mass generators, to the anyon model with free phase space that is a cotangent bundle of the Lobachevsky plane with twisted symplectic structure. Quantum mechanics of that model is described by irreducible representations of the (2+1)-dimensional Poincare' group.