Hamiltonian Mechanical Systems and Geometric Quantization:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1993
|
| Schriftenreihe: | Mathematics and Its Applications
260 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The book is a revised and updated version of the lectures given by the author at the University of Timi§oara during the academic year 1990-1991. Its goal is to present in detail some old and new aspects of the geometry of symplectic and Poisson manifolds and to point out some of their applications in Hamiltonian mechanics and geometric quantization. The material is organized as follows. In Chapter 1 we collect some general facts about symplectic vector spaces, symplectic manifolds and symplectic reduction. Chapter 2 deals with the study of Hamiltonian mechanics. We present here the general theory of Hamiltonian mechanicalsystems, the theory of the corresponding Poisson bracket and also some examples ofinfinite-dimensional Hamiltonian mechanical systems. Chapter 3 starts with some standard facts concerning the theory of Lie groups and Lie algebras and then continues with the theory ofmomentum mappings and the Marsden-Weinstein reduction. The theory of Hamilton-Poisson mechanical systems makes the object of Chapter 4. Chapter 5 js dedicated to the study of the stability of the equilibrium solutions of the Hamiltonian and the Hamilton Poisson mechanical systems. We present here some of the remarcable results due to Holm, Marsden, Ra~iu and Weinstein. Next, Chapter 6 and 7 are devoted to the theory of geometric quantization where we try to solve, in a geometrical way, the so called Dirac problem from quantum mechanics. We follow here the construction given by Kostant and Souriau around 1964 |
| Beschreibung: | 1 Online-Ressource (VIII, 280 p) |
| ISBN: | 9789401119924 9789401048804 |
| DOI: | 10.1007/978-94-011-1992-4 |
Internformat
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| 490 | 1 | |a Mathematics and Its Applications |v 260 | |
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Datensatz im Suchindex
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| author | Puta, Mircea |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| discipline | Physik Mathematik |
| doi_str_mv | 10.1007/978-94-011-1992-4 |
| format | Electronic eBook |
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| id | DE-604.BV042423871 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401119924 9789401048804 |
| language | English |
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| spelling | Puta, Mircea Verfasser aut Hamiltonian Mechanical Systems and Geometric Quantization by Mircea Puta Dordrecht Springer Netherlands 1993 1 Online-Ressource (VIII, 280 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 260 The book is a revised and updated version of the lectures given by the author at the University of Timi§oara during the academic year 1990-1991. Its goal is to present in detail some old and new aspects of the geometry of symplectic and Poisson manifolds and to point out some of their applications in Hamiltonian mechanics and geometric quantization. The material is organized as follows. In Chapter 1 we collect some general facts about symplectic vector spaces, symplectic manifolds and symplectic reduction. Chapter 2 deals with the study of Hamiltonian mechanics. We present here the general theory of Hamiltonian mechanicalsystems, the theory of the corresponding Poisson bracket and also some examples ofinfinite-dimensional Hamiltonian mechanical systems. Chapter 3 starts with some standard facts concerning the theory of Lie groups and Lie algebras and then continues with the theory ofmomentum mappings and the Marsden-Weinstein reduction. The theory of Hamilton-Poisson mechanical systems makes the object of Chapter 4. Chapter 5 js dedicated to the study of the stability of the equilibrium solutions of the Hamiltonian and the Hamilton Poisson mechanical systems. We present here some of the remarcable results due to Holm, Marsden, Ra~iu and Weinstein. Next, Chapter 6 and 7 are devoted to the theory of geometric quantization where we try to solve, in a geometrical way, the so called Dirac problem from quantum mechanics. We follow here the construction given by Kostant and Souriau around 1964 Mathematics Global analysis Global differential geometry Quantum theory Global Analysis and Analysis on Manifolds Applications of Mathematics Quantum Physics Differential Geometry Mathematik Quantentheorie Geometrische Quantisierung (DE-588)4156720-1 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 gnd rswk-swf Hamiltonsches System (DE-588)4139943-2 s Geometrische Quantisierung (DE-588)4156720-1 s DE-604 Mathematics and Its Applications 260 (DE-604)BV008163334 260 https://doi.org/10.1007/978-94-011-1992-4 Verlag Volltext |
| spellingShingle | Puta, Mircea Hamiltonian Mechanical Systems and Geometric Quantization Mathematics and Its Applications Mathematics Global analysis Global differential geometry Quantum theory Global Analysis and Analysis on Manifolds Applications of Mathematics Quantum Physics Differential Geometry Mathematik Quantentheorie Geometrische Quantisierung (DE-588)4156720-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| subject_GND | (DE-588)4156720-1 (DE-588)4139943-2 |
| title | Hamiltonian Mechanical Systems and Geometric Quantization |
| title_auth | Hamiltonian Mechanical Systems and Geometric Quantization |
| title_exact_search | Hamiltonian Mechanical Systems and Geometric Quantization |
| title_full | Hamiltonian Mechanical Systems and Geometric Quantization by Mircea Puta |
| title_fullStr | Hamiltonian Mechanical Systems and Geometric Quantization by Mircea Puta |
| title_full_unstemmed | Hamiltonian Mechanical Systems and Geometric Quantization by Mircea Puta |
| title_short | Hamiltonian Mechanical Systems and Geometric Quantization |
| title_sort | hamiltonian mechanical systems and geometric quantization |
| topic | Mathematics Global analysis Global differential geometry Quantum theory Global Analysis and Analysis on Manifolds Applications of Mathematics Quantum Physics Differential Geometry Mathematik Quantentheorie Geometrische Quantisierung (DE-588)4156720-1 gnd Hamiltonsches System (DE-588)4139943-2 gnd |
| topic_facet | Mathematics Global analysis Global differential geometry Quantum theory Global Analysis and Analysis on Manifolds Applications of Mathematics Quantum Physics Differential Geometry Mathematik Quantentheorie Geometrische Quantisierung Hamiltonsches System |
| url | https://doi.org/10.1007/978-94-011-1992-4 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT putamircea hamiltonianmechanicalsystemsandgeometricquantization |