Dirac Operators and Spectral Geometry

Giampiero Esposito

doi:10.1017/CBO9780511628795

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.

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

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Dirac Operators and Spectral Geometry

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Contents

Frontmatter
pp i-viii

Contents
pp ix-x

Preface
pp xi-xii

Acknowledgments
pp xiii-xiv

1 - The Dirac operator
pp 1-21

2 - Differential operators on manifolds
pp 22-40

3 - Index problems
pp 41-73

4 - Spectral asymmetry
pp 74-105

5 - Spectral geometry with operators of Laplace type
pp 106-147

6 - New frontiers
pp 148-190

References
pp 191-206

Index
pp 207-209

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