Group Theory A Physicist's Survey

ISBN-10: 0521896037
ISBN-13: 9780521896030
Edition: 2010
Authors: Pierre Ramond
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Book details

List price: $102.95
Copyright year: 2010
Publisher: Cambridge University Press
Publication date: 5/13/2010
Binding: Hardcover
Pages: 322
Size: 6.75" wide x 9.75" long x 0.75" tall
Weight: 1.694
Language: English

Preface: the pursuit of symmetries
Finite groups: an introduction
Group axioms
Finite groups of low order
Permutations
Basic concepts
Conjugation
Simple groups
Sylow's criteria
Semi-direct product
Young Tableaux
Finite groups: representations
Introduction
Schur's lemmas
The A<sub>4</sub> character table
Kronecker products
Real and complex representations
Embeddings
Z<sub>n</sub> character table
D<sub>n</sub> character table
Q<sub>2n</sub> character table
Some semi-direct products
Induced representations
Invariants
Coverings
Hilbert spaces
Finite Hilbert spaces
Fermi oscillators
Infinite Hilbert spaces
SU (2)
Introduction
Some representations
From Lie algebras to Lie groups
SU (2) &#8594; SU (1, 1)
Selected SU (2) applications
The isotropic harmonic oscillator
The Bohr atom
Isotopic spin
SU (3)
SU (3) algebra
�-Basis
�-Basis
�&#8242;-Basis
The triplet representation
The Chevalley basis
SU (3) in physics
The isotropic harmonic oscillator redux
The Elliott model
The Sakata model
The Eightfold Way
Classification of compact simple Lie algebras
Classification
Simple roots
Rank-two algebras
Dynkin diagrams
Orthonormal bases
Lie algebras: representation theory
Representation basics
A<sub>3</sub> fundamentals
The Weyl group
Orthogonal Lie algebras
Spinor representations
SO (2n) spinors
SO (2n + 1) spinors
Clifford algebra construction
Casimir invariants and Dynkin indices
Embeddings
Oscillator representations
Verma modules
Weyl dimension formula
Verma basis
Finite groups: the road to simplicity
Matrices over Galois fields
PSL<sub>2</sub> (7)
A doubly transitive group
Chevalley groups
A fleeting glimpse at the sporadic groups
Beyond Lie algebras
Serre presentation
Affine Kac-Moody algebras
Super algebras
The groups of the Standard Model
Space-time symmetries
The Lorentz and Poincar� groups
The conformal group
Beyond space-time symmetries
Color and the quark model
Invariant Lagrangians
Non-Abelian gauge theories
The Standard Model
Grand Unification
Possible family symmetries
Finite SU (2) and SO (3) subgroups
Finite SU (3) subgroups
Exceptional structures
Hurwitz algebras
Matrices over Hurwitz algebras
The Magic Square
Properties of some finite groups
Properties of selected Lie algebras
References
Index

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