Dirac Operators and Spectral Geometry

by Giampiero Esposito

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 nonlocal 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 invaluable reference to the Dirac operator and its applications in theoretical physics.

• Format: Paperback
• Language: English
• ISBN: 0521648629
• ISBN13: 9780521648622
• Release Date: September 1998
• Publisher: Cambridge University Press
• Length: 224 Pages
• Weight: 0.74 lbs.
• Dimensions: 0.5" x 6.0" x 9.0"