عنوان

Hamiltonian Mechanical Systems and Geometric Quantization

شابک

9401119929

شابک

9789401119924

شماره

b595742

عنوان اصلي

Hamiltonian Mechanical Systems and Geometric Quantization

نام عام مواد

[Book]

نام نخستين پديدآور

by Mircea Puta.

محل نشرو پخش و غیره

Dordrecht

نام ناشر، پخش کننده و غيره

Springer Netherlands

تاریخ نشرو بخش و غیره

1993

نام خاص و کميت اثر

(viii, 280 pages)

عنوان فروست

Mathematics and Its Applications, 260.

متن يادداشت

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.

متن يادداشت

This volume presents various aspects of the geometry of symplectic and Poisson manifolds, and applications in Hamiltonian mechanics and geometric quantization are indicated. Chapter 1 presents some general facts about symplectic vector space, symplectic manifolds and symplectic reduction. Chapter 2 deals with the study of Hamiltonian mechanics. Chapter 3 considers some standard facts concerning Lie groups and algebras which lead to the theory of momentum mappings and the Marsden--Weinstein reduction. Chapters 4 and 5 consider the theory and the stability of equilibrium solutions of Hamilton--Poisson mechanical systems. Chapters 6 and 7 are devoted to the theory of geometric quantization. This leads, in Chapter 8, to topics such as foliated cohomology, the theory of the Dolbeault--Kostant complex, and their applications. A discussion of the relation between geometric quantization and the Marsden--Weinstein reduction is presented in Chapter 9. The final chapter considers extending the theory of geometric quantization to Poisson manifolds, via the theory of symplectic groupoids. Each chapter concludes with problems and solutions, many of which present significant applications and, in some cases, major theorems. For graduate students and researchers whose interests and work involve symplectic geometry and Hamiltonian mechanics.

موضوع مستند نشده

Global analysis.

موضوع مستند نشده

Global differential geometry.

موضوع مستند نشده

Mathematics.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by Mircea Puta.

مستند نام اشخاص تاييد نشده

Mircea Puta

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y