Symmetries Shared by the Poincaré Group and the Poincaré Sphere

Symmetry

Young S. Kim¹ 

[1] Center for Fundamental Physics, University of Maryland, College Park, MD 20742, USA

关键词: Poincaré group;    Poincaré sphere;    Wigner’s little groups;    particle mass;    decoherence mechanism;    two-by-two representations;    Lorentz group;   

DOI  :  10.3390/sym5030233

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.