Pseudoclassical description of higher spins in $2+1$ dimensions

TL;DR

This paper introduces a pseudoclassical supersymmetric model for describing massive particles with higher spins in 2+1 dimensions, leading to a minimal quantum theory and connections to field theory, with extensions to 3+1 dimensions.

Contribution

It proposes a novel pseudoclassical supersymmetric framework for higher spins in 2+1 dimensions, deriving minimal quantum theories and relating to field equations, with dimensional reduction to 3+1 dimensions.

Findings

Derivation of Bargmann-Wigner equations for higher spins.

Explicit models for spin-1/2 and spin-1 particles.

Construction of a 3+1 dimensional higher spin Weyl particle model.

Abstract

Pseudoclassical supersymmetric model to describe massive particles with higher spins (integer and half-integer) in $2+1$ dimensions is proposed. The quantization of the model leads to the minimal (with only one polarization state) quantum theory. In particular, the Bargmann-Wigner type equations for higher spins arise in course of the canonical quantization. The cases of spin one-half and one are considered in detail. Here one gets Dirac particles and Chern-Simons particles respectively. A relation with the field theory is discussed. On the basis of the model proposed, and using dimensional reduction considerations, a model to describe Weyl particles with higher spins in $3+1$ dimensions is constructed.