Dirac operators and spectral geometry / Giampiero Esposito.
Material type: TextSeries: Cambridge lecture notes in physics ; 12.Publisher: Cambridge : Cambridge University Press, 1998Description: 1 online resource (xiii, 209 pages) : digital, PDF file(s)Content type:- text
- computer
- online resource
- 9780511628795 (ebook)
- Dirac Operators & Spectral Geometry
- 530.15/6362 21
- QC20.7.S64 E78 1998
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.
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