LEADER 03506oam 2200637 450 001 9910484527903321 005 20210624122010.0 010 $a1-280-63522-3 010 $a9786610635221 010 $a3-540-33421-1 024 7 $a10.1007/b138212 035 $a(CKB)1000000000282843 035 $a(SSID)ssj0000182959 035 $a(PQKBManifestationID)11198748 035 $a(PQKBTitleCode)TC0000182959 035 $a(PQKBWorkID)10194468 035 $a(PQKB)10583624 035 $a(DE-He213)978-3-540-33421-7 035 $a(MiAaPQ)EBC4643100 035 $a(MiAaPQ)EBC6463402 035 $a(PPN)123133513 035 $a(EXLCZ)991000000000282843 100 $a20210624d2006 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to symplectic Dirac operators /$fK. Habermann, L. Habermann 205 $a1st ed. 2006. 210 1$aBerlin, Germany :$cSpringer,$d[2006] 210 4$d©2006 215 $a1 online resource (XII, 125 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1887 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-33420-3 320 $aIncludes bibliographical references and index. 327 $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. 330 $aOne of the basic ideas in differential geometry is that the study of analytic properties of certain differential operators acting on sections of vector bundles yields geometric and topological properties of the underlying base manifold. Symplectic spinor fields are sections in an L^2-Hilbert space bundle over a symplectic manifold and symplectic Dirac operators, acting on symplectic spinor fields, are associated to the symplectic manifold in a very natural way. Hence they may be expected to give interesting applications in symplectic geometry and symplectic topology. These symplectic Dirac operators are called Dirac operators, since they are defined in an analogous way as the classical Riemannian Dirac operator known from Riemannian spin geometry. They are called symplectic because they are constructed by use of the symplectic setting of the underlying symplectic manifold. This volume is the first one that gives a systematic and self-contained introduction to the theory of symplectic Dirac operators and reflects the current state of the subject. At the same time, it is intended to establish the idea that symplectic spin geometry and symplectic Dirac operators may give valuable tools in symplectic geometry and symplectic topology, which have become important fields and very active areas of mathematical research. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1887 606 $aSymplectic and contact topology 606 $aSymplectic groups 606 $aSymplectic geometry 615 0$aSymplectic and contact topology. 615 0$aSymplectic groups. 615 0$aSymplectic geometry. 676 $a516.36 700 $aHabermann$b Katharina$f1966-$0298909 702 $aHabermann$b Lutz$f1959- 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bUtOrBLW 906 $aBOOK 912 $a9910484527903321 996 $aIntroduction to symplectic Dirac operators$9230575 997 $aUNINA