Helicity and Canonical Spin Operators of the Poincaré Algebra

Abstract

In the study of the irreducible unitary representations [m, s] of the Poincaré group, we define an ``helicity'' spin operator through a fundamental connection between canonical and helicity bases. This operator, in covariant notation, is simply related to the well‐known Bargmann‐Wigner operator and to the canonical spin operator. Its spatial components generate an SU(2)‐algebra and coincide with the elements of the Z‐spin algebra recently proposed on different grounds by Braathen‐Foldy. The very simple arguments developed here establish in a natural way the uniqueness of this algebra when helicity representations are studied.