An Introduction to Dirac Operators on Manifolds: v. 24 (Progress in Mathematical Physics) - Hardcover

Cnops, Jan

Hardcover

ISBN 10: 0817642986 ISBN 13: 9780817642983

Publisher: Birkhauser Boston Inc, 2002

Synopsis

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

About this title

Review

"The text should be accessible for senior undergraduate and graduate students. It requires very little previous knowledge of the domains covered. More advanced readers could perhaps appreciate the new approach to the theory as well as some new results on boundary value theory." —Mathematical Reviews "This book gives an introduction to Dirac operators on manifolds for readers with little knowledge in differential geometry and analysis.... Compared to other books treating similar subjects...the present book is considerably more elementary and is mostly restricted to results that can easily be obtained out of the definitions." —Zentralblatt Math "The extraordinary importance of Dirac operators in variuos domains of mathematics and physics is well known. So, although there are some remakrable monographs on Dirac operators, the high number of recent papers covering several subjects needs periodical surveys... The book is excellent for beginners offering several ideas of research and a global picture of a fascinating theory!"  ---Memoriile Sectiilor Stiintifice

Synopsis

Dirac operators play an important part in several domains of mathematics and mathematical physics, for example: index theory, theory of elliptic pseudodifferential operators, theory of electromagnetism, particle physics, and representation theory of Lie groups. In this work, the basic theories underlying the concept of Dirac operators are explored. Starting with the requisite material on Clifford algebras and differential geometry, the text focuses on the two main properties of Dirac operators: conformal invariance, which determines the local behavior of the operator, and the unique continuation property dominating global behavior. Spin groups and spin or bundles are covered, as well as the relations with their classical counterparts, orthogonal groups and Clifford bundles. The chapters on Clifford algebra and the fundamentals of differential geometry can be used as an introduction to the above topics, and are suitable for senior undergraduates and graduates. The other chapters are also accessible at this level.

Thus, 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. 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.

Edition details

• Publisher: Birkhauser Boston Inc
• Publication date: 2002
• Language: English
• ISBN 10: 0817642986
• ISBN 13: 9780817642983
• Binding: Hardcover
• Number of pages: 221