A Canonical Analysis of the Massless Superparticle

TL;DR

This paper analyzes the canonical structure of the massless superparticle in lower dimensions, revealing the nature of its fermionic constraints and deriving the associated local fermionic symmetry generator.

Contribution

It provides a detailed canonical analysis of the superparticle action, clarifying the role of first and second class constraints and deriving the fermionic symmetry generator.

Findings

Half of the fermionic constraints are first class after applying Dirac brackets.

The generator of the fermionic ppa-symmetry is explicitly derived.

The algebra of the ppa-symmetry generator is examined.

Abstract

The canonical structure of the action for a massless superparticle is considered in d = 2 + 1 and d = 3 + 1 dimensions. This is done by examining the contribution to the action of each of the components of the spinor {\theta} present; no attempt is made to maintain manifest covariance. Upon using the Dirac Bracket to eliminate the second class constraints arising from the canonical momenta associated with half of these components, we find that the remaining components have canonical momenta that are all first class constraints. From these first class constraints, it is possible to derive the generator of half of the local Fermionic {\kappa}-symmetry of Siegel; which half is contingent upon the choice of which half of the momenta associated with the components of {\theta} are taken to be second class constraints. The algebra of the generator of this Fermionic symmetry transformation is examined.