Group Theory: Birdtracks, Lie's, and Exceptional Groups - Couverture souple

Cvitanovic, Predrag

 
9780691202983: Group Theory: Birdtracks, Lie's, and Exceptional Groups
Couverture souple
ISBN 10 : 0691202982 ISBN 13 : 9780691202983
Editeur : Princeton University Press, 2020

Synopsis

If 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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À propos de l?auteur

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.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Princeton University Press
Date d'édition
2020
Langue
anglais
ISBN 10 
0691202982
ISBN 13 
9780691202983
Reliure
Broché
Nombre de pages
288
Coordonnées du fabricant
non disponible
Personne responsable
non disponible

Autres éditions populaires du même titre

9780691118369: Group Theory: Lie's, Tracks, And Exceptional Groups

Edition présentée

ISBN 10 :  0691118361 ISBN 13 :  9780691118369
Editeur : Princeton University Press, 2008
Couverture rigide