An Introduction to Dirac Operators on Manifolds

ISBN-13: 9781461265962 / Angielski / Miękka / 2012 / 211 str.

Jan Cnops

Opis

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

Recenzje

"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

Spis treści

Introduction * Clifford Algebras * Manifolds * Dirac Operators * Conformal Maps * Unique Continuation and the Cauchy Kernel * Boundary Values * Appendix. General Manifolds * The Additional Canterbury Tales * List of Symbols * Bibliography * Index

O autorze

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.