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Symmetries, Lie Algebras and Representations

Symmetries, Lie Algebras and Representations
A Graduate Course for Physicists


Part of Cambridge Monographs on Mathematical Physics

  • Date Published: October 2003
  • availability: Available
  • format: Paperback
  • isbn: 9780521541190

£ 67.99

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About the Authors
  • This is an introduction to Lie algebras and their applications in physics. The first three chapters show how Lie algebras arise naturally from symmetries of physical systems and illustrate through examples much of their general structure. Chapters 4 to 13 give a detailed introduction to Lie algebras and their representations, covering the Cartan-Weyl basis, simple and affine Lie algebras, real forms and Lie groups, the Weyl group, automorphisms, loop algebras and highest weight representations. Chapters 14 to 22 cover specific further topics, such as Verma modules, Casimirs, tensor products and Clebsch-Gordan coefficients, invariant tensors, subalgebras and branching rules, Young tableaux, spinors, Clifford algebras and supersymmetry, representations on function spaces, and Hopf algebras and representation rings. A detailed reference list is provided, and many exercises and examples throughout the book illustrate the use of Lie algebras in real physical problems. The text is written at a level accessible to graduate students, but will also provide a comprehensive reference for researchers.

    • Many exercises and tips
    • Clear pedagogical style with many exercises and extensive references
    • Fuchs is an experienced author with a very successful book in this area already published
    • 'Extras' available from the author's web site
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    Reviews & endorsements

    'One finds a striking wealth of material in this book … The reviewer wholeheartedly recommends this text to graduate students as well as to researchers in theoretical physics and related areas.' Acta. Sci. Math

    'The presentation of material is next to perfect, … this book may be considered as an excellent textbook … I agree with the authors that 'many readers will even use it as a reference tool for their whole professional life'.' Vladimir D. Ivashchuk, General Relativity and Gravitation

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    Product details

    • Date Published: October 2003
    • format: Paperback
    • isbn: 9780521541190
    • length: 464 pages
    • dimensions: 233 x 202 x 26 mm
    • weight: 0.83kg
    • contains: 36 b/w illus. 18 tables 188 exercises
    • availability: Available
  • Table of Contents

    1. Symmetries and conservation laws
    2. Basic examples
    3. The Lie algebra su(3) and hadron symmetries
    4. Formalization: algebras and Lie algebras
    5. Representations
    6. The Cartan-Weyl basis
    7. Simple and affine Lie algebras
    8. Real Lie algebras and real forms
    9. Lie groups
    10. Symmetries of the root system. The Weyl group
    11. Automorphisms of Lie algebras
    12. Loop algebras and central extensions
    13. Highest weight representations
    14. Verma modules, Casimirs, and the character formula
    15. Tensor products of representations
    16. Clebsch-Gordan coefficients and tensor operators
    17. Invariant tensors
    18. Subalgebras and branching rules
    19. Young tableaux and the symmetric group
    20. Spinors, Clifford algebras, and supersymmetry
    21. Representations on function spaces
    22. Hopf algebras and representation rings

  • Authors

    Jürgen Fuchs, Karlstads Universitet, Sweden

    Christoph Schweigert, Institut des Hautes Études Scientifiques, France

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