Pauli-Lubanski, Supertwistors, and the Superspinning Particle

TL;DR

This paper introduces a new super-Pauli-Lubanski pseudo-vector in 4D supersymmetry, derived from supertwistor constraints, and unifies results across dimensions using an Sl(2;K)-spinor formalism.

Contribution

It provides a novel construction of the super-Pauli-Lubanski vector from supertwistor constraints and unifies 4D, 3D, and 6D superspinning results with a spinor formalism.

Findings

Derived a super-Pauli-Lubanski pseudo-vector from supertwistor constraints.

Unified superspinning particle descriptions across dimensions using Sl(2;K)-spinor formalism.

Illustrated the construction with a classical superspin 1/2 particle model.

Abstract

We present a novel construction of the super-Pauli-Lubanski pseudo-vector for 4D supersymmetry and show how it arises naturally from the spin-shell constraints in the supertwistor formulation of superparticle dynamics. We illustrate this result in the context of a simple classical action for a "superspinning particle" of superspin 1/2. We then use an Sl(2;K)-spinor formalism for K=R,C,H to unify our 4D results with previous results for 3D and 6D (super)Pauli-Lubanski tensors.