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Hamiltonian Mechanical Systems and Geometric Quantization : Mathematics and Its Applications - Mircea Puta

Hamiltonian Mechanical Systems and Geometric Quantization

Mathematics and Its Applications

Hardcover Published: 30th June 1993
ISBN: 9780792323068
Number Of Pages: 280

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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 someold and new aspects ofthe geometry ofsymplectic 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 ofHamiltonian mechanics. We present here the gen­ eral theory ofHamiltonian mechanicalsystems, the theory ofthe corresponding Pois­ son 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 mechan­ ical 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 construc­ tion given by Kostant and Souriau around 1964.

Background Notation
Symplectic Geometry
Hamiltonian Mechanics
Lie Groups. Momentum Mappings. Reduction
Hamilton-Poisson Mechanics
Hamiltonian Mechanical Systems and Stability
Geometric Prequantization
Geometric Quantization
Foliated Cohomology and Geometric Quantization
Symplectic Reduction. Geometric Quantization. Constrained Mechanical Systems
Poisson Manifolds and Geometric Prequantization
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792323068
ISBN-10: 0792323068
Series: Mathematics and Its Applications
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 280
Published: 30th June 1993
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.5 x 15.5  x 1.7
Weight (kg): 0.59