An Introduction to Dirac Operators on Manifolds

Dirac operators play an important role in several domains of mathematics and mathematical physics. This book explores the basic theories underlying the concept of Dirac operators. Starting with preliminary material, it covers Clifford algebras, manifolds, conformal maps, unique continuation and the Cauchy kernel, and boundary values.

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The chapters on Clifford algebra and differential geometry can be used as an introduction to the topics, and are suitable for senior undergraduates and graduates. The other chapters are also accessible at this level.; This self-contained book requires very little previous knowledge of the domains covered, although the reader will benefit from knowledge of complex analysis, which gives the basic example of a Dirac operator.; The more advanced reader will appreciate the fresh approach to the theory, as well as the new results on boundary value theory.; Concise, but self-contained text at the introductory grad level. Systematic exposition.; Clusters well with other Birkhauser titles in mathematical physics.; Appendix. General Manifolds * List of Symbols * Bibliography * Index