Kinematic Explanation of Massless Particles Only Having Two Helicity   States
  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. 
Changli Liu and Fengjun Ge
physics.gen-ph