Birdtracks, Lie's, and Exceptional Groups
By (author) Predrag Cvitanovic
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Group Theory by Predrag Cvitanovic
Book DescriptionIf classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional. The invariant tensors are presented in a somewhat unconventional, but in recent years widely used, "birdtracks" notation inspired by the Feynman diagrams of quantum field theory. Notably, invariant tensor diagrams replace algebraic reasoning in carrying out all group-theoretic computations. The diagrammatic approach is particularly effective in evaluating complicated coefficients and group weights, and revealing symmetries hidden by conventional algebraic or index notations. The book covers most topics needed in applications from this new perspective: permutations, Young projection operators, spinorial representations, Casimir operators, and Dynkin indices. Beyond this well-traveled territory, more exotic vistas open up, such as "negative dimensional" relations between various groups and their representations. The most intriguing result of classifying primitive invariants is the emergence of all exceptional Lie groups in a single family, and the attendant pattern of exceptional and classical Lie groups, the so-called Magic Triangle. Written in a lively and personable style, the book is aimed at researchers and graduate students in theoretical physics and mathematics.
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Book DetailsISBN: 9780691118369
(229mm x 152mm x 23mm)
Imprint: Princeton University Press
Publisher: Princeton University Press
Publish Date: 1-Jul-2008
Country of Publication: United States
Books By Author Predrag Cvitanovic
Nonlinear Spatio-temporal Dynamics and Chaos in Semiconductors, Paperback (August 2005)
This book brings together concepts from semiconductor physics, nonlinear-dynamics and chaos to examine semiconductor transport phenomena.
Chaos, Scattering and Statistical Mechanics, Paperback (July 2005)
The first book about chaos in statistical mechanics, in Cambridge Nonlinear Science Series.
Universality in Chaos, Paperback (January 1989)» View all books by Predrag Cvitanovic
This book presents developments in the study of the chaotic behaviour of deterministic systems. It concentrates on the universal aspects of chaotic motions: those qualitative and quantitative predictions which apply to large classes of physical systems.
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Author Biography - Predrag Cvitanovic
Predrag Cvitanovic is the Glen P. Robinson Professor of Nonlinear Science at the Georgia Institute of Technology. He is the author of "Universality in Chaos" and lead author of the ChaosBook.org webbook.
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