Alex J. Dragt - A Lie connection between Hamiltonian and Lagrangian optics

dmtcs:238 - Discrete Mathematics & Theoretical Computer Science, January 1, 1997, Vol. 1 - https://doi.org/10.46298/dmtcs.238
A Lie connection between Hamiltonian and Lagrangian opticsArticle

Authors: Alex J. Dragt 1

  • 1 Department of Physics [College Park]

It is shown that there is a non-Hamiltonian vector field that provides a Lie algebraic connection between Hamiltonian and Lagrangian optics. With the aid of this connection, geometrical optics can be formulated in such a way that all aberrations are attributed to ray transformations occurring only at lens surfaces. That is, in this formulation there are no aberrations arising from simple transit in a uniform medium. The price to be paid for this formulation is that the Lie algebra of Hamiltonian vector fields must be enlarged to include certain non-Hamiltonian vector fields. It is shown that three such vector fields are required at the level of third-order aberrations, and sufficient machinery is developed to generalize these results to higher order.


Volume: Vol. 1
Published on: January 1, 1997
Imported on: March 26, 2015
Keywords: Hamiltonian and Lagrangian optics,Lie algebra,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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