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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
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An Introduction to Dirac Operators on Manifolds (Hardcover)
Loot Price: R1,956
Discovery Miles 19 560
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An Introduction to Dirac Operators on Manifolds (Hardcover)
Series: Progress in Mathematical Physics, v. 24
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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.
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