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020 _a9783540334217
_9978-3-540-33421-7
024 7 _a10.1007/b138212
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
072 7 _aPBMP
_2thema
082 0 4 _a516.36
_223
100 1 _aHabermann, Katharina.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aIntroduction to Symplectic Dirac Operators
_h[electronic resource] /
_cby Katharina Habermann, Lutz Habermann.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2006.
300 _aXII, 125 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1887
505 0 _aBackground 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.
520 _aOne 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. Hence 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.
650 0 _aGlobal differential geometry.
650 0 _aGlobal analysis.
650 1 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
700 1 _aHabermann, Lutz.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540822721
776 0 8 _iPrinted edition:
_z9783540334200
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1887
856 4 0 _uhttps://doi.org/10.1007/b138212
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11862
_d11862