Symplectic algebra and Gaussian optics
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.
KeywordsMathematical Method General Linear Simple groupS Symplectic groupS Linear Optic
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