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Symmetries, Lie Algebras and Representations - A Graduate Course for Physicists (Paperback, New Ed)
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Symmetries, Lie Algebras and Representations - A Graduate Course for Physicists (Paperback, New Ed)
Series: Cambridge Monographs on Mathematical Physics
Expected to ship within 12 - 19 working days
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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.
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