Spinning particles in $2+1$ dimensions

TL;DR

This paper develops Lagrangian and Hamiltonian formulations for free spinning particles, or anyons, in 2+1 dimensions, deriving two inequivalent models and analyzing their properties and differences from recent models.

Contribution

It introduces two new Lagrangian models for 2+1D anyons and compares their Hamiltonian structures, highlighting qualitative differences from existing models.

Findings

Two inequivalent Lagrangian formulations are derived.

Non-trivial Dirac brackets are computed for both models.

Differences with recent anyon models are identified.

Abstract

Lagrangian and Hamiltonian formulations of a free spinning particle in 2+1-dimensions or {\it anyon} are established, following closely the analysis of Hanson and Regge. Two viable (and inequivalent) Lagrangians are derived. It is also argued that one of them is more favourable. In the Hamiltonian analysis non-triviaal Dirac Brackets of the fundamental variables are computed for both the models. Important qualitative differences with a recently proposed model for anyons are pointed out.