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OverviewOne of the basic ideas in differential geometry is that the study of analytic properties of certain differential operators acting on sections of vector bundles yields geometric and topological properties of the underlying base manifold. Symplectic spinor fields are sections in an L^2-Hilbert space bundle over a symplectic manifold and symplectic Dirac operators, acting on symplectic spinor fields, are associated to the symplectic manifold in a very natural way. They may be expected to give interesting applications in symplectic geometry and symplectic topology. These symplectic Dirac operators are called Dirac operators, since they are defined in an analogous way as the classical Riemannian Dirac operator known from Riemannian spin geometry. They are called symplectic because they are constructed by use of the symplectic setting of the underlying symplectic manifold. This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research. Full Product DetailsAuthor: Katharina Habermann , Lutz HabermannPublisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Edition: 2006 ed. Volume: 1887 Dimensions: Width: 15.50cm , Height: 1.00cm , Length: 23.50cm Weight: 0.454kg ISBN: 9783540334200ISBN 10: 3540334203 Pages: 125 Publication Date: 26 July 2006 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsBackground on Symplectic Spinors.- Symplectic Connections.- Symplectic Spinor Fields.- Symplectic Dirac Operators.- An Associated Second Order Operator.- The Kähler Case.- Fourier Transform for Symplectic Spinors.- Lie Derivative and Quantization.ReviewsFrom the reviews: <p> The book starts with an introductory chapter which contains the background on symplectic spinors a ] . The book will be of interest to researchers working on symplectic geometry and /or symplectic topology, and in physicists interested to quantization. (Aurel Bejancu, Zentralblatt MATH, Vol. 1102 (4), 2007) From the reviews: The book starts with an introductory chapter which contains the background on symplectic spinors ! . The book will be of interest to researchers working on symplectic geometry and /or symplectic topology, and in physicists interested to quantization. (Aurel Bejancu, Zentralblatt MATH, Vol. 1102 (4), 2007) Author Information"Katharina Habermann is awarded by the ""Gerhard Hess Preis 2000"" -- a research prize of the German Research Foundation (DFG) for excellent young researchers." Tab Content 6Author Website:Countries AvailableAll regions |
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