Kepler Problem

Group Theoretical Aspects, Regularization and Quantization, with Application to the Study of Perturbations

Inbunden, Engelska, 2002

Av Bruno Cordani

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This work contains a comprehensive treatment of the Kepler problem, i.e. the two body problem. It is divided into four parts. In the first part the arguments are exposed elementarily and the properties of the problem are recovered in a purely conventional way. This part is written at undergraduate student level. In the second part, a unifying point of view is presented which centres the exposition on the intrinsic group-geometrical aspects. This part requires more mathematical background which is presented in the fourth part, in particular the basic tools of differential geometry and analytical mechanics used in the book. The third part exploits some results of the second part to give a geometrical description of the perturbation theory of the Kepler problem. Each of the four parts, which are to some extent independent, could form the basis for a one-semester course.

Produktinformation

Utgivningsdatum2002-12-11
Mått155 x 235 x 31 mm
Vikt857 g
FormatInbunden
SpråkEngelska
SerieProgress in Mathematical Physics
Antal sidor442
Upplaga2003
FörlagBirkhauser Verlag AG
ISBN9783764369026

Tillhör följande kategorier

Preface.- List of Figures.- 1 Introductory Survey.- 1.1 Part I - Elementary Theory.- 1.2 Part II - Group-Geometric Theory.- 1.3 Part III - Perturbation Theory.- 1.4 Part IV - Appendices.- I Elementary Theory 17.- 2 Basic Facts.- 3 Separation of Variables and Action-Angle Coordinates.- 4 Quantization of the Kepler Problem.- 5 Regularization and Symmetry.- II Group-Geometric Theory 109.- 6 Conformal Regularization.- 7 Spinorial Regularization.- 8 Return to Separation of Variables.- 9 Geometric Quantization.- 10 Kepler Problem with Magnetic Monopole.- III Perturbation Theory 235.- 11 General Perturbation Theory.- 12 Perturbations of the Kepler Problem.- 13 Perturbations with Axial Symmetry.- IV Appendices 321.- A Differential Geometry.- B Lie Groups and Lie Algebras.- C Lagrangian Dynamics.- D Hamiltonian Dynamics.