Hamiltonian Mechanical Systems and Geometric Quantization / by Mircea Puta
(Mathematics and Its Applications ; 260)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Dordrecht : Springer Netherlands : Imprint: Springer |
| 出版年 | 1993 |
| 本文言語 | 英語 |
| 大きさ | VIII, 280 p : online resource |
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| 内容注記 | 1 Symplectic Geometry 1.1 Symplectic Algebra 1.2 Symplectic Geometry 1.3 Darboux’s Theorem 1.4 Symplectic Reduction 1.5 Problems and Solutions 2 Hamiltonian Mechanics 2.1 Hamiltonian Mechanical Systems 2.2 Poisson Bracket 2.3 Infinite Dimensional Hamiltonian Mechanical Systems 2.4 Problems and Solutions 3 Lie Groups. Momentum Mappings. Reduction 3.1 Lie Groups 3.2 Actions of Lie Groups 3.3 The Momentum Mapping 3.4 Reduction of Symplectic Manifolds 3.5 Problems and Solutions 4 Hamilton-Poisson Mechanics 4.1 Poisson Geometry 4.2 The Lie-Poisson Structure 4.3 Hamilton-Poisson Mechanical Systems 4.4 Reduction of Poisson Manifolds 4.5 Problems and Solutions 5 Hamiltonian Mechanical Systems and Stability 5.1 The Meaning of Stability 5.2 Hamilton’s Equations and Stability 5.3 The Energy-Casimir Method 5.4 Problems and Solutions 6 Geometric Prequantization 6.1 Full Quantization and Dirac Problem 6.2 Complex Bundles and the Dirac Problem 6.3 Geometric Prequantization 6.4 Problems and Solutions 7 Geometric Quantization 7.1 Polarizations and the First Attempts to Quantization 7.2 Half-Forms Correction of Geometric Quantization 7.3 The Non-Existence Problem 7.4 Problems and Solutions 8 Foliated Cohomology and Geometric Quantization 8.1 Real Foliations and Differential Forms 8.2 Complex Foliations and Differential Forms 8.3 Complex Elliptic Foliations and Spectral Geometry 8.4 Cohomological Correction of Geometric Quantization 8.5 Problems and Solutions 9 Symplectic Reduction. Geometric Quantization. Constrained Mechanical Systems 9.1 Symplectic Reduction and Geometric Prequantization 9.2 Symplectic Reduction and Geometric Quantization 9.3 Applications to Constrained Mechanical Systems 9.4 Problems and Solutions 10 Poisson Manifolds and Geometric Prequantization 10.1 Groupoids 10.2 Symplectic Groupoids 10.3 Geometric Prequantization of Poisson Manifolds 10.4 Problems and Solutions References |
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| 著者標目 | *Puta, Mircea author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Applied mathematics LCSH:Engineering mathematics LCSH:Differential geometry LCSH:Quantum physics FREE:Mathematics FREE:Global Analysis and Analysis on Manifolds FREE:Applications of Mathematics FREE:Quantum Physics FREE:Differential Geometry |
| 分 類 | DC23:514.74 |
| 巻冊次 | ISBN:9789401119924 
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| ISBN | 9789401119924 |
| URL | http://dx.doi.org/10.1007/978-94-011-1992-4 |
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