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Variations on a theme by Kepler / Victor Guillemin and Shlomo Sternberg

Auteur principal : Guillemin, Victor, 1937-, AuteurCo-auteur : Sternberg, Shlomo, 1936-, AuteurType de document : MonographieCollection : Colloquium publications, 42Langue : anglais.Pays : Etats Unis.Éditeur : Providence, RI : American Mathematical Society, 1990Description : 1 vol. (II-88 p.) : ill. ; 26 cmISBN : 0821810421.ISSN : 0065-9258.Bibliographie : Bibliogr. p. 83-86. Index.Sujet MSC : 70F15, Mechanics of particles and systems -- Dynamics of a system of particles, including celestial mechanics, Celestial mechanics
81Rxx, Quantum theory, Groups and algebras in quantum theory
83C20, Relativity and gravitational theory -- General relativity, Classes of solutions; algebraically special solutions, metrics with symmetries
53C80, Differential geometry -- Global differential geometry, Applications to physics
70-02, Mechanics of particles and systems, Research exposition (monographs, survey articles)
En-ligne : Edition 2006 (Google) | Zentralblatt | MathSciNet
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Bibliogr. p. 83-86. Index

The theme of this book is the role of the symmetry Lie groups and Lie algebras in the explanation of the laws of classical and quantum physics, illustrated on the concrete situation of the classical Kepler motion, and of its quantum counterpart, the hydrogen atom. ... The study also includes the quantization of this manifold and the computation of the hydrogen spectrum, the derivation of the Kepler Hamiltonian from a geodesic flow in five dimension, etc. The intervention of the Minkowski space led to the final chapter of the book which studies homogeneous models in general relativity, and ends with a theory of Kostant, where electromagnetism and gravitation are unified in a Kaluza-Klein type theory in six dimensions. (Zentralblatt)

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