# Relativistic Anyon Beam: Construction and Properties

## TL;DR

This paper proposes a method to construct and analyze a relativistic anyon beam, deriving explicit solutions and currents, and discusses potential laboratory realization, advancing the understanding of anyon dynamics.

## Contribution

It introduces a novel construction of a relativistic anyon beam using superpositions of plane wave solutions, with explicit current expressions and property analysis.

## Key findings

- Derived explicit relativistic plane wave solutions for anyons.
- Constructed a planar anyon beam from superposed solutions.
- Analyzed the properties and currents of the proposed anyon beam.

## Abstract

Motivated by recent interest in photon and electron vortex beams, we propose the construction of a relativistic anyon beam. Following Jackiw and Nair [Phys. Rev. D 43, 1933 (1991)] we derive explicit form of relativistic plane wave solution of a single anyon. Subsequently we construct the planar anyon beam by superposing these solutions. Explicit expressions for the conserved anyon current are derived. Finally, we provide expressions for the anyon beam current using the superposed waves and discuss its properties. We also comment on the possibility of laboratory construction of anyon beam.