Poincare Sphere and a Unified Picture of Wigners Little Groups

It is noted that the Poincare sphere for polarization optics contains the symmetries of the Lorentz group. The sphere is thus capable of describing the internal space-time symmetries dictated by Wigners little groups. For massive particles, the little group is like the three-dimensional rotation group, while it is like the two-dimensional Euclidean group for massless particles. It is shown that the Poincare sphere, in addition, has a symmetry parameter corresponding to reducing the particle mass from a positive value to zero. The Poincare sphere thus the gives one unified picture of Wigners little groups for massive and massless particles.