2015/05/28 by Y. S. Kim, Kim, Y. S.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematics and Applications #Quantum Physics (quant-ph) #Relativity and Gravitational Theory #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1505.07715
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
arxiv created 2015/05/28 · openalex publication_date 2015/05/28 · arxiv updated 2015/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Henri Poincaré formulated the mathematics of the Lorentz transformations, known as the Poincaré group. He also formulated the Poincaré 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 Poincaré sphere contains the symmetry corresponding to the mass variation, leading to the O(3,2) symmetry. An illustrative calculation is given.