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

Maurice Kibler
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Maurice Kibler: IN2P3-CNRS et Université Claude Bernard, Institut de Physique Nucléaire de Lyon

A chapter in Symmetries in Science IX, 1997, pp 153-165 from Springer

Abstract: 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].

Keywords: Diophantine Equation; Schrodinger Equation; Compact Case; Quadratic Transformation; Hypercomplex Number (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4615-5921-4_11

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DOI: 10.1007/978-1-4615-5921-4_11

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