000 | 03439nam a22004815i 4500 | ||
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001 | 978-3-540-33421-7 | ||
003 | DE-He213 | ||
005 | 20190213151759.0 | ||
007 | cr nn 008mamaa | ||
008 | 100301s2006 gw | s |||| 0|eng d | ||
020 |
_a9783540334217 _9978-3-540-33421-7 |
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024 | 7 |
_a10.1007/b138212 _2doi |
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072 | 7 |
_aPBMP _2bicssc |
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_aMAT012030 _2bisacsh |
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072 | 7 |
_aPBMP _2thema |
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082 | 0 | 4 |
_a516.36 _223 |
100 | 1 |
_aHabermann, Katharina. _eauthor. _4aut _4http://id.loc.gov/vocabulary/relators/aut |
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245 | 1 | 0 |
_aIntroduction to Symplectic Dirac Operators _h[electronic resource] / _cby Katharina Habermann, Lutz Habermann. |
264 | 1 |
_aBerlin, Heidelberg : _bSpringer Berlin Heidelberg, _c2006. |
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300 |
_aXII, 125 p. _bonline resource. |
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336 |
_atext _btxt _2rdacontent |
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337 |
_acomputer _bc _2rdamedia |
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_aonline resource _bcr _2rdacarrier |
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_atext file _bPDF _2rda |
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490 | 1 |
_aLecture Notes in Mathematics, _x0075-8434 ; _v1887 |
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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 |
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856 | 4 | 0 | _uhttps://doi.org/10.1007/b138212 |
912 | _aZDB-2-SMA | ||
912 | _aZDB-2-LNM | ||
999 |
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