Spin and helicity of massive particles

TL;DR

This paper provides an alternative derivation of the relationship between spin and momentum orientation for massive particles using Wigner rotation, clarifying the Lorentz-invariance properties of helicity.

Contribution

It offers a new derivation of the angle between spin and momentum for massive particles, enhancing understanding of their Lorentz transformation properties.

Findings

Derived an alternative formula for the spin-momentum angle using Wigner rotation.

Clarified the Lorentz-invariance properties of helicity for massive particles.

Provided a detailed analysis of spin and helicity in relativistic contexts.

Abstract

It is a well-known fact that helicity is a Lorentz-invariant for massless but not for massive particles. Nevertheless, a satisfactory proof of this fact and a detailed analysis on the relative orientation between spin and the momentum are not readily available. One such analysis was presented by Wigner where a formula for the angle between the spin and the momentum is derived for massive particle states undergoing two successive boosts in orthogonal directions. In this note, using the Wigner rotation, an alternative derivation is provided.