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Symmetry 2013, 5(3), 233-252; doi:10.3390/sym5030233
Article

Symmetries Shared by the Poincaré Group and the Poincaré Sphere

1,*  and 2
Received: 29 May 2013 / Revised: 9 June 2013 / Accepted: 9 June 2013 / Published: 27 June 2013
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Abstract

Henri Poincaré formulated the mathematics of Lorentz transformations, known as the Poincaré group. He also formulated the Poincaré sphere for polarization optics. It is shown that these two mathematical instruments can be derived from the two-by-two representations of the Lorentz group. Wigner’s little groups for internal space-time symmetries are studied in detail. While the particle mass is a Lorentz-invariant quantity, it is shown to be possible to address its variations in terms of the decoherence mechanism in polarization optics.
Keywords: Poincaré group; Poincaré sphere; Wigner’s little groups; particle mass; decoherence mechanism; two-by-two representations; Lorentz group Poincaré group; Poincaré sphere; Wigner’s little groups; particle mass; decoherence mechanism; two-by-two representations; Lorentz group
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Kim, Y.S.; Noz, M.E. Symmetries Shared by the Poincaré Group and the Poincaré Sphere. Symmetry 2013, 5, 233-252.

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