Introduction to Symplectic Dirac Operators

• Main Authors: Habermann, Katharina (Author), Habermann, Lutz (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2006.
• Series: Lecture Notes in Mathematics, 1887
• Subjects: Mathematics.; Global analysis (Mathematics).; Manifolds (Mathematics).; Differential geometry.; Differential Geometry.; Global Analysis and Analysis on Manifolds.

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 b...

Table of Contents:

• 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.