An Introduction to Dirac Operators on Manifolds

By:

Jan Cnops

Format:

Paperback / softback

Series:

Progress in Mathematical Physics

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Description

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.

Release date Australia

November 1st, 2012

Author

Jan Cnops

Audience

Professional & Vocational

Edition

Softcover reprint of the original 1st ed. 2002

Illustrations

XI, 211 p.

Pages

211

Series

Progress in Mathematical Physics

Dimensions

155x235x12

ISBN-13

9781461265962

Product ID

21702099

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