Dirac operators and spectral geometry
著者
書誌事項
Dirac operators and spectral geometry
（Cambridge lecture notes in physics, 12）
Cambridge University Press, 1998
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注記
Includes bibliographical references (p. 191-206) and index
内容説明・目次
内容説明
The Dirac operator has many useful applications in theoretical physics and mathematics. This book provides a clear, concise and self-contained introduction to the global theory of the Dirac operator and to the analysis of spectral asymptotics with local or non-local boundary conditions. The theory is introduced at a level suitable for graduate students. Numerous examples are then given to illustrate the peculiar properties of the Dirac operator, and the role of boundary conditions in heat-kernel asymptotics and quantum field theory. Topics covered include the introduction of spin-structures in Riemannian and Lorentzian manifolds; applications of index theory; heat-kernel asymptotics for operators of Laplace type; quark boundary conditions; one-loop quantum cosmology; conformally covariant operators; and the role of the Dirac operator in some recent investigations of four-manifolds. This volume provides graduate students with a rigorous introduction and researchers with a valuable reference to the Dirac operator and its applications in theoretical physics.
目次
- 1. The Dirac operator
- 2. Differential operators on manifolds
- 3. Index problems
- 4. Spectral asymmetry
- 5. Spectral geometry with operators of Laplace type
- 6. New frontiers
- Appendices.
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