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Mathematics and Its Applications

By: Mircea Puta

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Hardcover | 30 June 1993

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Hardcover
292 Pages

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24.77 x 17.15 x 1.91

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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.

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You Can Find This Book In

Non-Fiction Mathematics Topology Geometry Differential & Riemannian Geometry Calculus & Mathematical Analysis Differential Calculus & Equations Applied Mathematics Numerical Analysis Science Physics Quantum Physics & Quantum Mechanics & Quantum Field Theory

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Paperback

Published: 5th November 2012

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Introduction
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
References
Index
Table of Contents provided by Blackwell. All Rights Reserved.

Mathematics and Its Applications

At a Glance

Hardcover

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Paperback

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