Kinematic Explanation of Massless Particles Only Having Two Helicity States

Abstract

Why massless particles, for example photons, can only have two helicity one-particle states is the main subject of this work. As we know, the little group which describes massive particle one-particle states' transformations under the Lorentz transformation is SO(3), while the little group describing massless states is ISO(2). In this paper, a method which is different from Inonu-Wigner contraction is used to contract SO(3) group to ISO(2) group. We use this contraction method to prove that the particle can only have two helicity one-particle states from the perspective of kinematics, when the particle mass tends to zero. Our proof is different from the dynamic explanation in the existing theories.