Relativistic particle dynamics in D=2+1

TL;DR

This paper introduces a supersymmetric action for massless spinning particles in 2+1 dimensions using twistor variables, analyzing constraints, equations of motion, and fractional spin states, with a potential massive extension.

Contribution

It presents a novel SUSY-invariant action for massless spinning particles in 2+1 dimensions incorporating twistor variables and explores fractional statistics and possible mass terms.

Findings

Particles exhibit fractional statistics and spin.

The action remains invariant under SUSY and reparametrizations.

A potential massive extension of the model is proposed.

Abstract

We propose a SUSY variant of the action for a massless spinning particles via the inclusion of twistor variables. The action is constructed to be invariant under SUSY transformations and $\tau$-reparametrizations even when an interaction field is including. The constraint analysis is achieved and the equations of motion are derived. The commutation relations obtained for the commuting spinor variables $\lambda$ show that the particle states have fractional statistics and spin. At once we introduce a possible massive term for the non-interacting model.