Dirac Operators and Spectral Geometry

A clear, concise and up-to-date introduction to the theory of the Dirac operator and its wide range of applications in theoretical physics for graduate students and researchers.

Giampiero Esposito (Author)

9780521648622, Cambridge University Press

Paperback, published 20 August 1998

224 pages
22.8 x 15.2 x 1.3 cm, 0.305 kg

"...a compendium of useful information, alternately in summary and detailed form, for mathematicians/mathematical physicists..." Mathematical Reviews

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.

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.

Subject Areas: Physics [PH], Probability & statistics [PBT]