Google full text of our books:


Group Theory:
Birdtracks, Lie's, and Exceptional Groups
Predrag Cvitanović

Hardcover | 2008 | $72.50 | £60.95 | ISBN: 9780691118369
288 pp. | 6 x 9 1/4 | 4000 birdtrack diagrams. 7 line illus. 31 tables.
Add to Shopping Cart

eBook | ISBN: 9781400837670 |
Our eBook editions are available from these online vendors

Reviews | Table of Contents
Introduction[PDF] pdf-icon

Google full text of this book:

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.


"This book has to be seen to be believed! The title, Group Theory, is nothing if not surprising, given that the material dealt with by Predrag Cvitanović in these roughly 250 pages requires a level of sophistication well beyond what is offered in the early stages of university algebra. In point of fact, the general theme of the book under review is Lie theory with representation theory in the foreground, and Cvitanović's revolutionary goal (e.g., 'birdtracks') and, for lack of a better word, the attendant combinatorics. . . . [F]or the right reader, which is to say, an R>0-linear combination of mathematician and physicist equipped with a zeal for novel combinatorics flavored diagram-gymnastics, this book will be a treat and a thrill, and its new and radical way to compute many things Lie is bound to make its mark."--Michael Berg, MAA Reviews

"More than just an innovative notation, this book offers a conceptually novel alternative path to a key mathematical result, the classification of finite-dimensional simple Lie algebras. . . . While this volume is an obvious resource for physics students, the traces of physics that remain in the work will elucidate for mathematics students how physics uses Lie groups as a tool."--D.V. Feldman, Choice

"I think that the book is a very interesting and thought provoking contribution to the literature on representations of compact Lie groups. It has many interesting original aspects that deserve to be known much better than they are."--Karl-Hermann Neeb, Journal of the Lie Theory

"[T]he narrative of the book is written in a relaxed and witty style. The book is intriguing as well as entertaining."--Jeb F. Willenbring, Mathematical Reviews


More Endorsements

Table of Contents

Subject Areas:


Shopping Cart options:

  • For ebooks:

Our eBook editions are available
from these online vendors:

  • Amazon Kindle Store
  • Google Play eBook Store
  • Many of our ebooks are available through
    library electronic resources including these platforms:

  • Books at JSTOR
  • Ebrary
  • Ebook Library
  • EBSCO Ebooks
  • MyiLibrary
  • Dawsonera (UK)

    • For hardcover/paperback orders in United States, Canada, Latin America, Asia, and Australia

     Hardcover : $72.50 ISBN: 9780691118369

    Add to shopping cart
    View contents of your shopping cart

    • For hardcover/paperback orders in Europe, Africa, the Middle East, India, and Pakistan

     Hardcover  £60.95 ISBN: 9780691118369

    Add to shopping cart
    View contents of your shopping cart

    Prices subject to change without notice

    File created: 7/11/2017

    Questions and comments to:
    Princeton University Press

    New Book E-mails
    New In Print
    PUP Blog
    Princeton APPS
    Sample Chapters
    Princeton Legacy Library
    Exam/Desk Copy
    Recent Awards
    Princeton Shorts
    Freshman Reading
    PUP Europe
    About Us
    Contact Us
    PUP Home

    Bookmark and Share 
    Send me emails
    about new books in:
    More Choices