Group Theory

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A01=Predrag Cvitanovic
Adjoint
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Analytic continuation
Antisymmetric tensor
Antisymmetrizer
Author_Predrag Cvitanovic
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Betti number
Big O notation
Bilinear form
Calculation
Category1=Non-Fiction
Category=PBG
Category=PHQ
Characteristic equation
Classical group
Coefficient
Combination
Computation
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Coset
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Diagram (category theory)
Dimension
Diophantine equation
Dynkin index
E6 (mathematics)
E7 (mathematics)
E8 (mathematics)
Eigenvalues and eigenvectors
Eightfold Way (physics)
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Feynman diagram
Fock space
Gamma function
General linear group
Global symmetry
Group theory
Hurwitz's theorem (composition algebras)
Infinitesimal transformation
Invariant theory
Irreducible representation
Kronecker delta
Language_English
Levi-Civita symbol
Lie algebra
Lie group
Linear map
Magic square
Mathematical induction
Maximal set
Minkowski space
Non-associative algebra
Notation
Octonion
Orthogonality
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Permutation
Polynomial
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Projection (linear algebra)
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Regular representation
Semisimple Lie algebra
Simple Lie group
Skew-symmetric matrix
softlaunch
Special case
Spin group
Spinor
Structure constants
Subgroup
Subset
Summation
Symmetric group
Symmetrization
Symplectic group
Tensor
Theorem
Trace (linear algebra)
Transpose
Young tableau

Product details

  • ISBN 9780691202983
  • Dimensions: 156 x 235mm
  • Publication Date: 26 May 2020
  • Publisher: Princeton University Press
  • Publication City/Country: US
  • Product Form: Paperback
  • Language: English
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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.

Predrag Cvitanović 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.