A Simple Action for a Free Anyon

TL;DR

This paper introduces a new, simple classical action for free anyons in 2+1 dimensions derived from realizations of the sl(2,R) algebra, revealing phenomena like Zitterbewegung and connecting to existing models.

Contribution

It presents a novel, straightforward classical action for free anyons based on classical realizations of the sl(2,R) algebra, expanding the theoretical framework.

Findings

Derived a continuous family of actions for free anyons

Identified Zitterbewegung in solutions of the equations of motion

Connected new actions to existing literature at the classical level

Abstract

By studying classical realizations of the sl(2,R) algebra in a two dimensional phase space $(q,\pi)$, we have derived a continuous family of new actions for free anyons in 2+1 dimensions. For the case of light-like spin vector $(S_\mu S^\mu =0)$, the action is remarkably simple. We show the appearence of the Zitterbewegung in the solutions of the equations of motion, and relate the actions to others in the literature at classical level.