Following closely the Kline-Kay derivation of Lunebourg's method, the author shows that for isotropic media the spinor formalism of the optics field supplies a new mathematical formulation of classical geometrical optics with in addition polarization and transport equations for the electric and magnetic fields. This new theory, not so complete as the Kline-Kay theory is much easier to handle and could be of interest in some optical systems where polarization variations are important.
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Pïerre Hillion (1979) studied this question.