An Introduction to Dirac Operators on Manifolds

Jan Cnops

ISBN 10: 1461265967 / ISBN 13: 9781461265962

Editore: Birkhäuser Boston, Birkhäuser Boston Nov 2012, 2012

Riguardo questo articolo

Neuware -Dirac operators play an important role in several domains ofmathematics and physics, for example: index theory, ellipticpseudodifferential operators, electromagnetism, particle physics, andthe representation theory of Lie groups.In this essentially self-contained work, the basic ideas underlyingthe concept of Dirac operators are explored. Starting with Cliffordalgebras and the fundamentals of differential geometry, the textfocuses on two main properties, namely, conformal invariance, whichdetermines the local behavior of the operator, and the uniquecontinuation property dominating its global behavior. Spin groups andspinor bundles are covered, as well as the relations with theirclassical counterparts, orthogonal groups and Clifford bundles.The chapters on Clifford algebras and the fundamentals ofdifferential geometry can be used as an introduction to the abovetopics, and are suitable for senior undergraduate and graduatestudents. The other chapters are also accessible at this level so thatthis text requires very little previous knowledge of the domainscovered. The reader will benefit, however, from some knowledge ofcomplex analysis, which gives the simplest example of a Diracoperator. More advanced readers---mathematical physicists, physicistsand mathematicians from diverse areas---will appreciate the freshapproach to the theory as well as the new results on boundary valuetheory.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 228 pp. Englisch.

Codice articolo 9781461265962

Dati bibliografici

• Titolo: An Introduction to Dirac Operators on Manifolds
• Editore: Birkhäuser Boston, Birkhäuser Boston Nov 2012
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461265967
• ISBN 13: 9781461265962
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

Dirac operators play an important role in several domains of mathematics and mathematical physics. In this self-contained text, the basic theories underlying the concept of Dirac operators are explored. Starting with preliminary material, the book covers Clifford algebras, manifolds, conformal maps, unique continuation and the Cauchy kernel, and boundary values. Only real analysis is required, although complex analysis is helpful. A good textbook for senior undergrad and graduate students, it will also be a useful resource for math physicists and theoretical physicists.

Recensione

"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