Abstract

Duality principles are derived that apply to any first-order system. Both symplectic and nonsymplectic duality transformations are studied. Duality permits a significant simplification for classifying first-order systems as well as proving operator relations for such systems. As an example of this technique operator relations for three dimensions are analyzed. Laplacian and Fourier duals are defined, and the completeness of this approach is explicitly proved for two-dimensional first-order systems; this approach yields the first complete classification to our knowledge of ISP(4, C), the complex, inhomogeneous four-dimensional, symplectic group.

© 1990 Optical Society of America

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