Poincaré Sphere and a Unified Picture of Wigner’s Little Groups
Department of Physics, University of Maryland, College Park, Maryland, 20742, U.S.A.
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Published online: 25 September 2014
It is noted that the Poincaré 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 Wigner’s 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 Poincaré sphere, in addition, has a symmetry parameter corresponding to reducing the particle mass from a positive value to zero. The Poincaré sphere thus the gives one unified picture of Wigner’s little groups for massive and massless particles.
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