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Hamiltonian Mechanical Systems and Geometric Quantization (Hardcover, 1993 ed.)
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Hamiltonian Mechanical Systems and Geometric Quantization (Hardcover, 1993 ed.)
Series: Mathematics and Its Applications, 260
Expected to ship within 12 - 17 working days
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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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