%0 Journal Article
%T Symmetries Shared by the Poincar¨¦ Group and the Poincar¨¦ Sphere
%A Young S. Kim
%A Marilyn E. Noz
%J Symmetry
%D 2013
%I MDPI AG
%R 10.3390/sym5030233
%X Henri Poincar¨¦ formulated the mathematics of Lorentz transformations, known as the Poincar¨¦ group. He also formulated the Poincar¨¦ 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.
%K Poincar¨¦ group
%K Poincar¨¦ sphere
%K Wigner¡¯s little groups
%K particle mass
%K decoherence mechanism
%K two-by-two representations
%K Lorentz group
%U http://www.mdpi.com/2073-8994/5/3/233