| An Introduction to Dirac Operators on Manifolds Contributor(s): Cnops, Jan (Author) |
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ISBN: 0817642986 ISBN-13: 9780817642983 Publisher: Springer OUR PRICE: $94.05 Product Type: Hardcover - Other Formats Published: July 2002 Annotation: 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. |
| Additional Information |
| BISAC Categories: - Mathematics | Algebra - Linear - Medical - Mathematics | Group Theory |
| Dewey: 512.57 |
| LCCN: 2002025563 |
| Series: Progress in Mathematical Physics |
| Physical Information: 0.62" H x 6.84" W x 9.02" (1.09 lbs) 228 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 gi |