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Harmonic Maps, Loop Groups, and Integrable Systems : London Mathematical Society Student Texts - Martin A. Guest

Harmonic Maps, Loop Groups, and Integrable Systems

London Mathematical Society Student Texts

Hardcover

Published: 13th January 1997
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This is an accessible introduction to some of the fundamental connections among differential geometry, Lie groups, and integrable Hamiltonian systems. The text demonstrates how the theory of loop groups can be used to study harmonic maps. By concentrating on the main ideas and examples, the author leads up to topics of current research. The book is suitable for students who are beginning to study manifolds and Lie groups, and should be of interest both to mathematicians and to theoretical physicists as well.

'... an accessible introduction to some of the fundamental connections beween differental geometry, Lie groups and integrable Hamiltonian systems.' L'Enseignement Mathematique 'It is very rare to find a book that can take a student from the very basics of a subject to the frontiers of active research. The author is to be congratulated on having produced just such a rarity!' Bulletin of the London Mathematics Society 'The book will certainly be appreciated by mathematicians as well as theoretical physics interested in the subject.' European Mathematical Society

Preface
Acknowledgements
One-Dimensional Integrable Systems
Lie groups
Lie algebras
Factorizations and homogeneous spaces
Hamilton's equations and Hamiltonian systems
Lax equations
Adler-Kostant-Symes
Adler-Kostant-Symes (continued)
Concluding remarks on one-dimensional Lax equations
Two-Dimensional Integrable Systems
Zero-curvature equations
Some solutions of zero-curvature equations
Loop groups and loop algebras
Factorizations and homogeneous spaces
The two-dimensional Toda lattice
T-functions and the Bruhat decomposition
Solutions of the two-dimensional Toda lattice
Harmonic maps from C to a Lie group G
Harmonic maps from C to a Lie group (continued)
Harmonic maps from C to a symmetric space
Harmonic maps from C to a symmetric space (continued)
Application: harmonic maps from S2 to CPn
Primitive maps
Weierstrass formulae for harmonic maps
One-Dimensional and Two-Dimensional Integrable Systems
From 2 Lax equations to 1 zero-curvature equation
Harmonic maps of finite type
Application: harmonic maps from T2 to S2
Epilogue
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521580854
ISBN-10: 0521580854
Series: London Mathematical Society Student Texts
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 212
Published: 13th January 1997
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.6
Weight (kg): 0.48