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On Quadratic and Nonquadratic Forms: Application to R2m→R2m-n Nonbijective Transformations

In: Symmetries in Science IX

Author

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  • Maurice Kibler

    (IN2P3-CNRS et Université Claude Bernard, Institut de Physique Nucléaire de Lyon)

Abstract

The application of (Hopf) fiber bundles is well developed in theoretical and mathematical physics [1,2]. Along this vein, the Hopf fibrations on spheres lead to nonbijective canonical quadratic transformations useful in classical and quantum mechanics [3–13]. The Hopf fibrations on spheres, as well as their extensions on hyperboloids [10], yield the concepts of “constraint Lie algebra” and “Lie algebra under constraints”, which are of importance for connecting invariance or noninvariance algebras of dynamical systems [11].

Suggested Citation

  • Maurice Kibler, 1997. "On Quadratic and Nonquadratic Forms: Application to R2m→R2m-n Nonbijective Transformations," Springer Books, in: Bruno Gruber & Michael Ramek (ed.), Symmetries in Science IX, pages 153-165, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-5921-4_11
    DOI: 10.1007/978-1-4615-5921-4_11
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