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Symmetries Shared by the Poincaré Group and the Poincaré Sphere
Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA
Department of Radiology, New York University, New York, NY 10016, USA
* Author to whom correspondence should be addressed.
Received: 29 May 2013; in revised form: 9 June 2013 / Accepted: 9 June 2013 / Published: 27 June 2013
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
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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.
Kim YS, Noz ME. Symmetries Shared by the Poincaré Group and the Poincaré Sphere. Symmetry. 2013; 5(3):233-252.
Kim, Young S.; Noz, Marilyn E. 2013. "Symmetries Shared by the Poincaré Group and the Poincaré Sphere." Symmetry 5, no. 3: 233-252.