Symplectic algebra and Gaussian optics

  • H. G. Helfenstein
Brief Reports


We show that the passage from Gaussian (i.e. axially symmetrical) optics to general linear optics is not a true generalization, except for few “degenerate” cases with isolated pairs of conjugate planes. In other words: For the effects of geometrical first order optics one can replace the symplectic groupS p(4, ℝ) by the simpler groupS L(2, ℝ) without loss of generality. This is achieved by classifying all cases arising from the use ofS p(4, ℝ) in optics.


Mathematical Method General Linear Simple groupS Symplectic groupS Linear Optic 


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  1. [1]
    V. Guillemin and S. Sternberg, Symplectic Techniques in Physics, Cambridge 1984.Google Scholar
  2. [2]
    M. Born and E. Wolf, Principles of Optics, Pergamon, Oxford 1980.Google Scholar

Copyright information

© Birkhäuser Verlag 1988

Authors and Affiliations

  • H. G. Helfenstein
    • 1
  1. 1.Dept. of Mathematics & StatisticsCarleton UniversityOttawaCanada

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