Kinematic Explanation of Massless Particles Only Having Two Helicity States

TL;DR

This paper provides a kinematic explanation for why massless particles like photons only have two helicity states, using a novel group contraction method from SO(3) to ISO(2) to demonstrate this property.

Contribution

It introduces a new contraction method from SO(3) to ISO(2) to explain the helicity state limitation of massless particles from a kinematic perspective.

Findings

Massless particles have only two helicity states due to group contraction.

The method differs from dynamic explanations in existing theories.

Provides a purely kinematic proof for helicity state limitation.

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.