Dirac Operators and Spectral Geometry

by Giampiero Esposito

Overview

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.

Product Details

ISBN-13:	9780521648622
Publisher:	Cambridge University Press
Publication date:	08/20/1998
Series:	Cambridge Lecture Notes in Physics , #12
Pages:	224
Product dimensions:	5.98(w) x 8.98(h) x 0.51(d)

Table of Contents

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.

Editorial Reviews

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

From the Publisher