TY  - BOOK
AU  - Habermann,Katharina
AU  - Habermann,Lutz
ED  - SpringerLink (Online service)
TI  - Introduction to Symplectic Dirac Operators
T2  - Lecture Notes in Mathematics,
SN  - 9783540334217
AV  - QA641-670 
U1  - 516.36 23
PY  - 2006///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Global analysis
KW  - Global differential geometry
KW  - Differential Geometry
KW  - Global Analysis and Analysis on Manifolds
N1  - Background 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
N2  - One 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
UR  - http://dx.doi.org/10.1007/b138212
ER  -