Franklin

Dirac operators in Riemannian geometry / Thomas Friedrich ; translated by Andreas Nestke.

Author/Creator:
Friedrich, Thomas, 1949-
Standardized Title:
Dirac-Operatoren in der Riemannschen Geometrie. English
Publication:
Providence, Rhode Island : American Mathematical Society, [2000]
Series:
Graduate studies in mathematics ; v. 25.
Graduate studies in mathematics, 1065-7339 ; volume 25
Format/Description:
Book
1 online resource (213 p.)
Subjects:
Geometry, Riemannian.
Dirac equation.
Form/Genre:
Electronic books.
Language:
English
Contents:
""Cover""; ""Title""; ""Copyright""; ""Contents""; ""Introduction""; ""Chapter 1. Clifford Algebras and Spin Representation""; ""1.1. Linear algebra of quadratic forms""; ""1.2. The Clifford algebra of a quadratic form""; ""1.3. Clifford algebras of real negative definite quadratic forms""; ""1.4. The pin and the spin group""; ""1.5. The spin representation""; ""1.6. The group Spin[sup(C)]""; ""1.7. Real and quaternionic structures in the space of n-spinors""; ""1.8. References and exercises""; ""Chapter 2. Spin Structures""; ""2.1. Spin structures on SO(n)-principal bundles""
""2.2. Spin structures in covering spaces""""2.3. Spin structures on G-principal bundles""; ""2.4. Existence of spin[sup(C)] structures""; ""2.5. Associated spinor bundles""; ""2.6. References and exercises""; ""Chapter 3. Dirac Operators""; ""3.1. Connections in spinor bundles""; ""3.2. The Dirac and the Laplace operator in the spinor bundle""; ""3.3. The Schrodinger-Lichnerowicz formula""; ""3.4. Hermitian manifolds and spinors""; ""3.5. The Dirac operator of a Riemannian symmetric space""; ""3.6. References and Exercises""; ""Chapter 4. Analytical Properties of Dirac Operators""
""4.1. The essential self-adjointness of the Dirac Operator in L[sup(2)]""""4.2. The spectrum of Dirac operators over compact manifolds""; ""4.3. Dirac operators are Fredholm operators""; ""4.4. References and Exercises""; ""Chapter 5. Eigenvalue Estimates for the Dirac Operator and Twistor Spinors""; ""5.1. Lower estimates for the eigenvalues of the Dirac operator""; ""5.2. Riemannian manifolds with Killing spinors""; ""5.3. The twistor equation""; ""5.4. Upper estimates for the eigenvalues of the Dirac operator""; ""5.5. References and Exercises""; ""Appendix A. Seiberg-Witten Invariants""
""B.7. Frobenius' theorem""""B.8. The Freudenthal-Yamabe theorem""; ""B.9. Holonomy theory""; ""B.10. References""; ""Bibliography""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""K""; ""L""; ""M""; ""N""; ""P""; ""Q""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""; ""Y""; ""Z""; ""Back Cover""
Notes:
Description based upon print version of record.
Includes bibliographical references and index.
Description based on print version record.
Contributor:
Nestke, Andreas, translator.
ISBN:
1-4704-2080-5
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