We use the results of a recent reformulation of the theory of arbitrary-order differential equations in terms of non-Hermitian operators to show that the invariant binorm is associated to a generalized Courant-Snyder invariant. Furthermore, we indicate the existence of higher-order invariants associated to the Casimir operators of the group, utilized to treat higher-order equations. We also discuss the intrinsic supersymmetric nature of the theory developed. Finally, we show the relevance of the proposed mathematical technique to the design of fiberoptics transport systems.
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Dattoli, G., Loreto, V., Mari, C. et al. Biunitary transformations and ordinary differential equations.—II. Nuovo Cim B 106, 1375–1390 (1991). https://doi.org/10.1007/BF02728367
- Ordinary differential equations
- Infinite-dimensional Lie groups
- PACS 42.10
- Propagation and transmission in homogeneous media
- Particle beams and particle optics