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Applications of the Fundamental Theorems of Projective and Affine Geometry in Physics

  • Piotr Kielanowski
  • Anatol Odzijewicz
  • Emma Previato
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

The closely related fundamental theorems of projective and affine geometry are keys to understanding some important but seemingly unrelated topics in mathematical physics. Specifically, they can be used in proofs of Wigner’s theorem on ray correspondences in quantum mechanics and also to establish the scale extended Poincaré group as the basic causality preserving symmetry group of special relativity. We describe these two theorems and show their roles in establishing the just mentioned results.

Keywords

Wigner’s theorem Alexandrov–Zeeman Theorem. 

Mathematics Subject Classification (2000)

Primary 51N10 51N15 Secondary 83A05 81Pxx. 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Piotr Kielanowski
    • 1
  • Anatol Odzijewicz
    • 2
  • Emma Previato
    • 3
  1. 1.Departamento de FísicaCINVESTAVCiudad de MéxicoMexico
  2. 2.Institute of MathematicsUniversity of BialystokBialystokPoland
  3. 3.Department of Mathematics and StatisticsBoston UniversityBostonUSA

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