Comments on spin operators and spin-polarization states of 2+1 fermions

TL;DR

This paper discusses spin polarization operators and states of 2+1 dimensional massive Dirac fermions, introducing a 4-spinor representation that facilitates the definition of a conserved covariant spin operator and links to the pseudoclassical limit.

Contribution

It introduces a 4-spinor representation for 2+1 fermions that enables a covariant spin operator and clarifies the connection between quantum and pseudoclassical models.

Findings

Introduction of a 4-spinor representation for 2+1 fermions.

Definition of a conserved covariant spin operator.

Connection between quantum operators and pseudoclassical models.

Abstract

In this brief article we discuss spin polarization operators and spin polarization states of 2+1 massive Dirac fermions and find a convenient representation by the help of 4-spinors for their description. We stress that in particular the use of such a representation allows us to introduce the conserved covariant spin operator in the 2+1 field theory. Another advantage of this representation is related to the pseudoclassical limit of the theory. Indeed, quantization of the pseudoclassical model of a spinning particle in 2+1 dimensions leads to the 4-spinor representation as the adequate realization of the operator algebra, where the corresponding operator of a first-class constraint, which cannot be gauged out by imposing the gauge condition, is just the covariant operator previously introduced in the quantum theory.