English

The O(3,2) Symmetry derivable from the Poincar\'e Sphere

Mathematical Physics 2015-05-29 v1 High Energy Physics - Theory math.MP Quantum Physics

Abstract

Henri Poincar\'e formulated the mathematics of the Lorentz transformations, known as the Poincar\'e group. He also formulated the Poincar\'e sphere for polarization optics. It is noted that his sphere contains the symmetry of the Lorentz group applicable to the momentum-energy four-vector of a particle in the Lorentz-covariant world. Since the particle mass is a Lorentz-invariant quantity, the Lorentz group does not allow its variations. However, the Poincar\'e sphere contains the symmetry corresponding to the mass variation, leading to the O(3,2)O(3,2) symmetry. An illustrative calculation is given.

Keywords

Cite

@article{arxiv.1505.07715,
  title  = {The O(3,2) Symmetry derivable from the Poincar\'e Sphere},
  author = {Y. S. Kim},
  journal= {arXiv preprint arXiv:1505.07715},
  year   = {2015}
}

Comments

LaTex 14 pages, 1 figure, included in the Nova Editorial Book: Relativity, Gravitation, Cosmology: Foundations, edited by Valeriy Dvoeglazov (2015). arXiv admin note: text overlap with arXiv:1203.4539