Lie Algebras in Particle Physics: From Isospin to Unified Theories (Google eBook)

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Westview Press, Oct 1, 1999 - Mathematics - 344 pages
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Howard Georgi is the co-inventor (with Sheldon Glashow) of the SU(5) theory. This extensively revised and updated edition of his classic text makes the theory of Lie groups accessible to graduate students, while offering a perspective on the way in which knowledge of such groups can provide an insight into the development of unified theories of strong, weak, and electromagnetic interactions.
  

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Contents

103 Irreducible representations and symmetry
140
104 Invariant tensors
141
106 Triality
143
108 Normalization
144
109 Tensor operators
145
1011 The weights of n m
146
1012 Generalization of WignerEckart
152
1013 Tensors for SU2
154

19 Useful theorems
11
110 Subgroups
12
111 Schurs lemma
14
112 Orthogonality relations
18
113 Characters
21
114 Eigenstates
26
115 Tensor products
27
116 Example of tensor products
28
117 Finding the normal modes
30
118 Symmetries of 2n+1gons
34
119 Permutation group on n objects
35
120 Conjugacy classes
36
121 Young tableaux
38
122 Example our old friend
39
Lie Groups
44
22 Lie algebras
46
23 The Jacobi identity
48
24 The adjoint representation
49
25 Simple algebras and groups
52
26 States and operators
53
27 Fun with exponentials
54
SU2
57
32 Raising and lowering operators
58
33 The standard notation
61
34 Tensor products
64
35 J₃ values add
65
Tensor Operators
69
42 Using tensor operators
70
43 The WignerEckart theorem
71
44 Example
73
45 Making tensor operators
76
46 Products of operators
78
Isospin
80
52 Creation operators
81
53 Number operators
83
55 Symmetry of tensor products
84
56 The deuteron
85
57 Superselection rules
86
58 Other particles
87
59 Approximate isospin symmetry
89
Roots and Weights
91
62 More on the adjoint representation
92
63 Roots
93
64 Raising and lowering
94
66 Watch carefully this is important
96
SU3
99
72 Weights and roots of SU3
101
Simple Roots
103
82 Simple roots
105
83 Constructing the algebra
108
84 Dynkin diagrams
111
G₂
112
87 The Cartan matrix
114
88 Finding all the roots
115
89 The SU 2s
117
810 Constructing the G₂ algebra
118
the algebra C₃
120
812 Fundamental weights
121
813 The trace of a generator
123
More SU3
125
92 Constructing the states
127
93 The Weyl group
130
94 Complex conjugation
131
95 Examples of other representations
132
Tensor Methods
138
102 Tensor components and wave functions
139
1014 ClebschGordan coefficients from tensors
156
1015 Spin 𝑠₁ + 𝑠₂ 1
157
1016 Spin 𝑠₁+ 𝑠₂ _ k
160
Hypercharge and Strangeness
166
112 The GellMann Okubo formula
169
113 Hadron resonances
173
114 Quarks
174
Young Tableaux
178
122 ClebschGordan decomposition
180
123 SU3 SU2 x U1
183
SUN
187
132 SUN tensors
190
133 Dimensions
193
134 Complex representations
194
135 SUN SUM SUN + M
195
3D Harmonic Oscillator
198
142 Angular momentum
200
SU6 and the Quark Model
205
152 SUN SUM SUNM
206
153 The baryon states
208
154 Magnetic moments
210
Color
214
162 Quantum Chromodynamics
218
163 Heavy quarks
219
Constituent Quarks
221
Unified Theories and SU5
225
182 Parity violation helicity and handedness
226
183 Spontaneously broken symmetry
228
184 Physics of spontaneous symmetry breaking
229
185 Is the Higgs real?
230
186 Unification and SUb
231
187 Breaking SU5
234
188 Proton decay
235
The Classical Groups
237
192 The S02n + 1 algebras
238
193 The Sp2n algebras
239
194 Quaternions
240
The Classification Theorem
244
202 Regular subalgebras
251
203 Other Subalgebras
253
21 SO2n+ and Spinors
255
212 Real and pseudoreal
259
213 Real representations
261
214 Pseudoreal representations
262
22 SO2n + 2 Spinors
265
SUn SO2n
270
232 𝛤𝒎 and R as invariant tensors
272
233 Products of 𝛤s
274
234 Selfduality
277
SO10
279
241 SO10 and SU4 x SU2 x SU2
282
242 Spontaneous breaking of SO10
285
244 Breaking SO10 SU3 x SU2 x U1
287
245 Breaking SO 10 SU3 x U1
289
Automorphisms
291
252 Fun with SO8
293
26 Sp2n
297
262 Tensors for Sp2n
299
27 Odds and Ends
302
272 E₆ unification
304
273 Breaking E₆
308
275 Anomalies
309
Epilogue
311
Index
312
Copyright

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Page vi - Frontiers in Physics David Pines, Editor Volumes of the Series published from 1961 to 1973 are not officially numbered. The parenthetical numbers shown are designed to aid librarians and bibliographers to check the completeness of their holdings. Titles published in this series prior to 1987 appear under either the WA Benjamin or the Benjamin/Cummings imprint; titles published since 1986 appear under the Addison-Wesley imprint.
Page vii - Current, 1967 Current Algebras and Applications to Particle Physics, 1968 Nuclear Theory: The Quasiparticle Method, 1968 The Quark Model, 1969 Approximation Methods in Quantum Mechanics, 1969 Nonlinear Plasma Theory, 1969 Quantum Kinematics and Dynamics, 1970 Statistical Mechanics: A Set of Lectures...
Page vi - Concepts in Solids: Lectures on the Theory of Solids, 1963 Regge Poles and S-Matrix Theory, 1963 Electron Scattering and Nuclear and Nucleon Structure: A Collection of Reprints with an Introduction, 1963 Nuclear Theory: Pairing Force Correlations to Collective Motion, 1964 Mandelstam Theory and Regge Poles: An Introduction M. Froissart for Experimentalists, 1963 Complex Angular Momenta and Particle Physics...
Page vi - A Lecture Note and Reprint Volume, 1961 Quantum Electrodynamics: A Lecture Note and Reprint Volume The Theory of Fundamental Processes: A Lecture Note Volume, 1961 Problem in Quantum Theory of Many-Particle Systems: A Lecture Note and Reprint Volume, 1961 The Many-Body Problem: A Lecture Note and Reprint Volume, 1961 The Mossbauer Effect: A Review With a Collection of Reprints, 1962 Quantum Statistical Mechanics: Green's Function Methods in Equilibrium and Nonequilibrium Problems, 1962 Paramagnetic...
Page vi - David Pines, Editor Volumes of the Series published from 1961 to 1973 are not officially numbered. The parenthetical numbers shown are designed to aid librarians and bibliographers to check the completeness of their holdings. Titles published in this series prior to 1987 appear under either the WA Benjamin or the Benjamin/Cummings imprint; titles published since 1986 appear under the Westview Press imprint. 1, 2.
Page vii - Interactions, 1972 Combinatorics and Renormalization in Quantum Field Theory, 1973 The Redshift Controversy, 1973 Hadron Physics at Very High Energies, 1973 Basic Principles of Plasma Physics: A Statistical Approach, 1973 (2nd printing, with revisions, 1980) The Physical Principles of Electron Paramagnetic Resonance, 2nd Edition, completely revised, enlarged, and reset, 1973 [cf. (9) — 1st edition Volumes published from 1974 onward are being numbered as an integral part of the bibliography.
Page vii - Phase Transitions, 1965 An Introduction to the Theory of Superfluidity, 1965 Superconductivity of Metals and Alloys, 1966 Pseudopotentials in the Theory of Metals, 1966 Phenomenological Theories of High Energy Scattering: An Experimental Evaluation, 1967 The Anharmonic Crystal, 1967 Augmented Plane Wave Method: A Guide to...
Page vi - N. Bloembergen Nuclear Magnetic Relaxation: A Reprint Volume, 1961 S-Matrix Theory of Strong Interactions: A Lecture Note and Reprint Volume, 1961 Quantum Electrodynamics: A Lecture Note and Reprint Volume, 1961 The Theory of Fundamental Processes: A Lecture Note...
Page viii - Phillips 72. T. Tajima 73. W. Kruer 74. P. Ramond 75. BF Hatfield 76. P. Sokolsky 77. R. Field 80. JF Gunion HE Haber G. Kane S. Dawson 81. RC Davidson 82. E. Fradkin 83.
Page vi - The Eightfold Way (A Review— With a Collection of Reprints), 1964 Strong-Interaction Physics: A Lecture Note Volume, 1964 Theory of Interacting Fermi Systems, 1964 Theory of Superconductivity, 1964 (revised 3rd printing.

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About the author (1999)

Howard Georgi is professor of physics at Harvard University.

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