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Dispersion Operators Algebra and Linear Canonical Transformations

2017; Springer Science+Business Media; Volume: 56; Issue: 4 Linguagem: Inglês

10.1007/s10773-016-3268-4

0020-7748

Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Randriamisy Hasimbola Damo Emile, Hanitriarivo Rakotoson,

Nonlinear Waves and Solitons

This work intends to present a study on relations between a Lie algebra called dispersion operators algebra, linear canonical transformation and a phase space representation of quantum mechanics that we have introduced and studied in previous works. The paper begins with a brief recall of our previous works followed by the description of the dispersion operators algebra which is performed in the framework of the phase space representation. Then, linear canonical transformations are introduced and linked with this algebra. A multidimensional generalization of the obtained results is given.