The Relativistic Spherical Top as a Massive Twistor

TL;DR

This paper demonstrates the equivalence between the spherical top and massive twistor models for spinning particles in special relativity, and shows that the twistor model reproduces known scattering amplitude spectra.

Contribution

It establishes a Hamiltonian formulation linking the spherical top and twistor models, incorporating Regge trajectories and confirming consistency with amplitude descriptions.

Findings

Equivalence between spherical top and twistor models proven.

Dirac brackets computed for physical phase space.

Quantization matches known scattering amplitude spectra.

Abstract

We prove the equivalence between two traditional approaches to the classical mechanics of a massive spinning particle in special relativity. One is the spherical top model of Hanson and Regge, recast in a Hamiltonian formulation with improved treatment of covariant spin constraints. The other is the massive twistor model, slightly generalized to incorporate the Regge trajectory relating the mass to the total spin angular momentum. We establish the equivalence by computing the Dirac brackets of the physical phase space carrying three translation and three rotation degrees of freedom. Lorentz covariance and little group covariance uniquely determine the structure of the physical phase space. The Regge trajectory does not affect the phase space but enters the equations of motion. Upon quantization, the twistor model produces a spectrum that agrees perfectly with the massive spinor-helicity description proposed by Arkani-Hamed, Huang and Huang for scattering amplitudes for all masses and spins.