Group Theory : A Physicist's Survey - Pierre Ramond

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Group Theory

A Physicist's Survey

By: Pierre Ramond

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Hardcover | 13 May 2010

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Hardcover
322 Pages

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24.5 x 18 x 3

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Group theory has long been an important computational tool for physicists, but with the advent of the Standard Model it has become a powerful conceptual tool as well. This book introduces physicists to many of the fascinating mathematical aspects of group theory, and mathematicians to its physics applications.

Designed for advanced undergraduate and graduate students, this book gives a comprehensive overview of the main aspects of both finite and continuous group theory, with an emphasis on applications to fundamental physics. Finite groups are extensively discussed, highlighting their irreducible representations and invariants. Lie algebras, and to a lesser extent Kac-Moody algebras, are treated in detail, including Dynkin diagrams. Special emphasis is given to their representations and embeddings. The group theory underlying the Standard Model is discussed, along with its importance in model building. Applications of group theory to the classification of elementary particles are treated in detail.

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"The books construction is straightforward... Group Theory: A Physicist's Survey successfully introduces physics model builder to the most likely toold os choice for future constructions." Robert Gilmore, Physics Today

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You Can Find This Book In

Non-Fiction Mathematics Groups & Group Theory Engineering & Technology Technology in General Maths for Engineers Science Physics Mathematical Physics Algebra Applied Mathematics

Preface: the pursuit of symmetries	p. 1
Finite groups: an introduction	p. 4
Group axioms	p. 5
Finite groups of low order	p. 6
Permutations	p. 19
Basic concepts	p. 22
Conjugation	p. 22
Simple groups	p. 25
Sylow's criteria	p. 27
Semi-direct product	p. 28
Young Tableaux	p. 31
Finite groups: representations	p. 33
Introduction	p. 33
Schur's lemmas	p. 35
The A₄ character table	p. 41
Kronecker products	p. 44
Real and complex representations	p. 46
Embeddings	p. 48
Z_n character table	p. 52
D_n character table	p. 53
Q_2n character table	p. 56
Some semi-direct products	p. 58
Induced representations	p. 61
Invariants	p. 64
Coverings	p. 67
Hilbert spaces	p. 69
Finite Hilbert spaces	p. 69
Fermi oscillators	p. 70
Infinite Hilbert spaces	p. 72
SU (2)	p. 78
Introduction	p. 78
Some representations	p. 82
From Lie algebras to Lie groups	p. 86
SU (2) → SU (1, 1)	p. 89
Selected SU (2) applications	p. 93
The isotropic harmonic oscillator	p. 93
The Bohr atom	p. 95
Isotopic spin	p. 99
SU (3)	p. 102
SU (3) algebra	p. 102
-Basis	p. 106
-Basis	p. 107
′-Basis	p. 108
The triplet representation	p. 110
The Chevalley basis	p. 112
SU (3) in physics	p. 114
The isotropic harmonic oscillator redux	p. 114
The Elliott model	p. 115
The Sakata model	p. 117
The Eightfold Way	p. 118
Classification of compact simple Lie algebras	p. 123
Classification	p. 124
Simple roots	p. 129
Rank-two algebras	p. 131
Dynkin diagrams	p. 134
Orthonormal bases	p. 140
Lie algebras: representation theory	p. 143
Representation basics	p. 143
A₃ fundamentals	p. 144
The Weyl group	p. 149
Orthogonal Lie algebras	p. 151
Spinor representations	p. 153
SO (2n) spinors	p. 154
SO (2n + 1) spinors	p. 156
Clifford algebra construction	p. 159
Casimir invariants and Dynkin indices	p. 164
Embeddings	p. 168
Oscillator representations	p. 178
Verma modules	p. 180
Weyl dimension formula	p. 187
Verma basis	p. 188
Finite groups: the road to simplicity	p. 190
Matrices over Galois fields	p. 192
PSL₂ (7)	p. 197
A doubly transitive group	p. 198
Chevalley groups	p. 201
A fleeting glimpse at the sporadic groups	p. 205
Beyond Lie algebras	p. 208
Serre presentation	p. 208
Affine Kac-Moody algebras	p. 210
Super algebras	p. 216
The groups of the Standard Model	p. 221
Space-time symmetries	p. 222
The Lorentz and Poincaré groups	p. 223
The conformal group	p. 231
Beyond space-time symmetries	p. 235
Color and the quark model	p. 239
Invariant Lagrangians	p. 240
Non-Abelian gauge theories	p. 243
The Standard Model	p. 244
Grand Unification	p. 246
Possible family symmetries	p. 249
Finite SU (2) and SO (3) subgroups	p. 249
Finite SU (3) subgroups	p. 252
Exceptional structures	p. 254
Hurwitz algebras	p. 254
Matrices over Hurwitz algebras	p. 257
The Magic Square	p. 259
Properties of some finite groups	p. 265
Properties of selected Lie algebras	p. 277
References	p. 307
Index	p. 308
Table of Contents provided by Ingram. All Rights Reserved.

Group Theory

A Physicist's Survey

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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