Alternative approaches to the Casalbuoni-Brink-Schwarz Superparticle

TL;DR

This paper applies Wigner's method to the super-Poincare group to develop a general framework for superparticles, showing the Casalbuoni-Brink-Schwarz superparticle as a special case and reformulating it as a gauge theory.

Contribution

It introduces a new approach to superparticle theory using Wigner's method, Clifford vacua, and a vielbein formalism, unifying and extending previous models.

Findings

Superparticle's spin operator obeys Wigner's constraints.

Casalbuoni-Brink-Schwarz superparticle is a special case of the general construction.

The theory can be reformulated as a gauge theory with a gauge symmetry related to spin constraints.

Abstract

Wigner's method of induced representations is applied to the N=1 super-Poincare group, and by using a state corresponding to the basic vector of the little group as a Clifford vacuum we show that the spin operator of a supersymmetric point particle obeys Wigner's constraints. As dynamical variables for the particle we use canonical coordinates on the symmetry group manifold. The physical phase space is then constructed using a vielbein formalism. We find that the Casalbuoni-Brink-Schwarz superparticle appears as a special case of our general construction. Finally, the theory is reformulated as a gauge theory where the gauge freedom corresponds to the choice of spin constraints or, equivalently, the free choice of relativistic center of mass. In a special case the gauge symmetry reduces to the well known kappa-symmetry.