Why Group Theory?p. 1 Finite Groupsp. 2 Groups and representationsp. 2 Example - Z[subscript 3]p. 3 The regular representationp. 4 Irreducible representationsp. 5 Transformation groupsp. 6 Application: parity in quantum mechanicsp. 7 Example: S[subscript 3]p. 8 Example: addition of integersp. 9 Useful theoremsp. 10 Subgroupsp. 11 Schur's lemmap. 13 * Orthogonality relationsp. 17 Charactersp. 20 Eigenstatesp. 25 Tensor productsp. 26 Example of tensor productsp. 27 * Finding the normal modesp. 29 * Symmetries of 2n+1-gonsp. 33 Permutation group on n objectsp. 34 Conjugacy classesp. 35 Young tableauxp. 37 Example -- our old friend S[subscript 3]p. 38 Another example -- S[subscript 4]p. 38 * Young tableaux and representations of S[subscript n]p. 38 Lie Groupsp. 43 Generatorsp. 43 Lie algebrasp. 45 The Jacobi identityp. 47 The adjoint representationp. 48 Simple algebras and groupsp. 51 States and operatorsp. 52 Fun with exponentialsp. 53 SU(2)p. 56 J[subscript 3] eigenstatesp. 56 Raising and lowering operatorsp. 57 The standard notationp. 60 Tensor productsp. 63 J[subscript 3] values addp. 64 Tensor Operatorsp. 68 Orbital angular momentump. 68 Using tensor operatorsp. 69 The Wigner-Eckart theoremp. 70 Examplep. 72 * Making tensor operatorsp. 75 Products of operatorsp. 77 Isospinp. 79 Charge independencep. 79 Creation operatorsp. 80 Number operatorsp. 82 Isospin generatorsp. 82 Symmetry of tensor productsp. 83 The deuteronp. 84 Superselection rulesp. 85 Other particlesp. 86 Approximate isospin symmetryp. 88 Perturbation theoryp. 88 Roots and Weightsp. 90 Weightsp. 90 More on the adjoint representationp. 91 Rootsp. 92 Raising and loweringp. 93 Lots of SU(2)sp. 93 Watch carefully - this is important!p. 95 SU(3)p. 98 The Gell-Mann matricesp. 98 Weights and roots of SU(3)p. 100 Simple Rootsp. 103 Positive weightsp. 103 Simple rootsp. 105 Constructing the algebrap. 108 Dynkin diagramsp. 111 Example: G[subscript 2]p. 112 The roots of G[subscript 2]p. 112 The Cartan matrixp. 114 Finding all the rootsp. 115 The SU(2)sp. 117 Constructing the G[subscript 2] algebrap. 118 Another example: the algebra C[subscript 3]p. 120 Fundamental weightsp. 121 The trace of a generatorp. 123 More SU(3)p. 125 Fundamental representations of SU(3)p. 125 Constructing the statesp. 127 The Weyl groupp. 130 Complex conjugationp. 131 Examples of other representationsp. 132 Tensor Methodsp. 138 Lower and upper indicesp. 138 Tensor components and wave functionsp. 139 Irreducible representations and symmetryp. 140 Invariant tensorsp. 141 Clebsch-Gordan decompositionp. 141 Trialityp. 143 Matrix elements and operatorsp. 143 Normalizationp. 144 Tensor operatorsp. 145 The dimension of (n,m)p. 145 * The weights of (n,m)p. 146 Generalization of Wigner-Eckartp. 152 * Tensors for SU(2)p. 154 * Clebsch-Gordan coefficients from tensorsp. 156 * Spin s[subscript 1] + s[subscript 2] - 1p. 157 * Spin s[subscript 1] + s[subscript 2] - kp. 160 Hypercharge and Strangenessp. 166 The eight-fold wayp. 166 The Gell-Mann Okubo formulap. 169 Hadron resonancesp. 173 Quarksp. 174 Young Tableauxp. 178 Raising the indicesp. 178 Clebsch-Gordan decompositionp. 180 SU(3) [right arrow] SU(2) [times] U(1)p. 183 SU(N)p. 187 Generalized Gell-Mann matricesp. 187 SU(N) tensorsp. 190 Dimensionsp. 193 Complex representationsp. 194 SU(N) [multiply sign in circle] SU(M) [set membership] SU(N +M)p. 195 3-D Harmonic Oscillatorp. 198 Raising and lowering operatorsp. 198 Angular momentump. 200 A more complicated examplep. 200 SU(6) and the Quark Modelp. 205 Including the spinp. 205 SU(N) [multiply sign in circle] SU(M) [set membership] SU(NM)p. 206 The baryon statesp. 208 Magnetic momentsp. 210 Colorp. 214 Colored quarksp. 214 Quantum Chromodynamicsp. 218 Heavy quarksp. 219 Flavor SU(4) is useless!p. 219 Constituent Quarksp. 221 The nonrelativistic limitp. 221 Unified Theories and SU(5)p. 225 Grand unificationp. 225 Parity violation, helicity and handednessp. 226 Spontaneously broken symmetryp. 228 Physics of spontaneous symmetry breakingp. 229 Is the Higgs real?p. 230 Unification and SU(5)p. 231 Breaking SU(5)p. 234 Proton decayp. 235 The Classical Groupsp. 237 The SO(2n) algebrasp. 237 The SO(2n + 1) algebrasp. 238 The Sp(2n) algebrasp. 239 Quaternionsp. 240 The Classification Theoremp. 244 II-systemsp. 244 Regular subalgebrasp. 251 Other Subalgebrasp. 253 SO(2n + 1) and Spinorsp. 255 Fundamental weight of SO(2n + 1)p. 255 Real and pseudo-realp. 259 Real representationsp. 261 Pseudo-real representationsp. 262 R is an invariant tensorp. 262 The explicit form for Rp. 262 SO(2n + 2) Spinorsp. 265 Fundamental weights of SO(2n + 2)p. 265 SU(n) [subset or is implied by] SO(2n)p. 270 Clifford algebrasp. 270 [Gamma][subscript m] and R as invariant tensorsp. 272 Products of [Gamma][subscript s]p. 274 Self-dualityp. 277 Example: SO(10)p. 279 The SU(n) subalgebrap. 279 SO(10)p. 282 SO(10) and SU(4) [times] SU(2) [times] SU(2)p. 282 * Spontaneous breaking of SO(10)p. 285 * Breaking SO(10) [right arrow] SU(5)p. 285 * Breaking SO(10) [right arrow] SU(3) [times] SU(2) [times] U(1)p. 287 * Breaking SO(10) [right arrow] SU(3) [times] U(1)p. 289 * Lepton number as a fourth colorp. 289 Automorphismsp. 291 Outer automorphismsp. 291 Fun with SO(8)p. 293 Sp(2n)p. 297 Weights of SU(n)p. 297 Tensors for Sp(2n)p. 299 Odds and Endsp. 302 Exceptional algebras and octoniansp. 302 E[subscript 6] unificationp. 304 Breaking E[subscript 6]p. 308 SU(3) [times] SU(3) [times] SU(3) unificationp. 308 Anomaliesp. 309 Epiloguep. 311 Indexp. 312 Table of Contents provided by Syndetics. 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