An Introduction to Dirac Operators on Manifolds

  • Jan Cnops

Part of the Progress in Mathematical Physics book series (PMP, volume 24)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Jan Cnops
    Pages 1-24
  3. Jan Cnops
    Pages 25-60
  4. Jan Cnops
    Pages 61-89
  5. Jan Cnops
    Pages 91-121
  6. Jan Cnops
    Pages 145-169
  7. Back Matter
    Pages 171-211

About this book

Introduction

Dirac operators play an important role in several domains of mathematics and physics, for example: index theory, elliptic pseudodifferential operators, electromagnetism, particle physics, and the representation theory of Lie groups. In this essentially self-contained work, the basic ideas underlying the concept of Dirac operators are explored. Starting with Clifford algebras and the fundamentals of differential geometry, the text focuses on two main properties, namely, conformal invariance, which determines the local behavior of the operator, and the unique continuation property dominating its global behavior. Spin groups and spinor bundles are covered, as well as the relations with their classical counterparts, orthogonal groups and Clifford bundles. The chapters on Clifford algebras and the fundamentals of differential geometry can be used as an introduction to the above topics, and are suitable for senior undergraduate and graduate students. The other chapters are also accessible at this level so that this text requires very little previous knowledge of the domains covered. The reader will benefit, however, from some knowledge of complex analysis, which gives the simplest example of a Dirac operator. More advanced readers---mathematical physicists, physicists and mathematicians from diverse areas---will appreciate the fresh approach to the theory as well as the new results on boundary value theory.

Keywords

Complex analysis applications of mathematics curvature differential geometry group lie groups manifold mathematical physics

Authors and affiliations

  • Jan Cnops
    • 1
  1. 1.Department of Computer SciencesGent PolytechnicGentBelgium

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-0065-9
  • Copyright Information Birkhäuser Boston 2002
  • Publisher Name Birkhäuser, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4612-6596-2
  • Online ISBN 978-1-4612-0065-9
  • About this book