Group Theory
eBook - PDF

Group Theory

Birdtracks, Lie's, and Exceptional Groups

  1. 288 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Group Theory

Birdtracks, Lie's, and Exceptional Groups

About 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.

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Yes, you can access Group Theory by Predrag Cvitanović in PDF and/or ePUB format, as well as other popular books in Mathematics & Group Theory. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Contents
  3. Acknowledgments
  4. Chapter 1. Introduction
  5. Chapter 2. A preview
  6. Chapter 3. Invariants and reducibility
  7. Chapter 4. Diagrammatic notation
  8. Chapter 5. Recouplings
  9. Chapter 6. Permutations
  10. Chapter 7. Casimir operators
  11. Chapter 8. Group integrals
  12. Chapter 9. Unitary groups
  13. Chapter 10. Orthogonal groups
  14. Chapter 11. Spinors
  15. Chapter 12. Symplectic groups
  16. Chapter 13. Negative dimensions
  17. Chapter 14. Spinors’ symplectic sisters
  18. Chapter 15. SU(n) family of invariance groups
  19. Chapter 16. G[sub(2)] family of invariance groups
  20. Chapter 17. E[sub(8)] family of invariance groups
  21. Chapter 18. E[sub(6)] family of invariance groups
  22. Chapter 19. F[sub(4)] family of invariance groups
  23. Chapter 20. E[sub(7)] family and its negative-dimensional cousins
  24. Chapter 21. Exceptional magic
  25. Appendix A. Recursive decomposition
  26. Appendix B. Properties of Young projections
  27. Bibliography
  28. Index