Twistors and the massive spinning particle

TL;DR

This paper develops gauge-invariant twistor variables for the massive spinning particle across dimensions D=3,4,6, revealing insights into its quantum spin properties and consistency conditions.

Contribution

It introduces a new twistor formulation for the massive spinning particle with extended supersymmetry, clarifying its Lorentz invariance and quantum consistency.

Findings

Quantum N=2 particle has spin 0 or 1

N>2 is quantum inconsistent in D=4,6

Twistor variables simplify analysis of spinning particles

Abstract

Gauge-invariant twistor variables are found for the massive spinning particle with N-extended local worldline supersymmetry, in spacetime dimensions D=3,4,6. The twistor action is manifestly Lorentz invariant but the anticommuting spin variables appear exactly as in the non-relativistic limit. This allows a simple confirmation that the quantum N=2 spinning particle has either spin one or spin zero, and that N>2 is quantum inconsistent for D=4,6.