| Preface | p. xiii |
| Acknowledgements | p. xiv |
| An introduction to unitary symmetry | |
| The search for higher symmetries | p. 1 |
| The eight-baryon puzzle | p. 1 |
| The elimination of G[subscript 0] | p. 4 |
| SU(3) and its representations | p. 5 |
| The representations of SU(n) | p. 5 |
| The representations of SU(2) | p. 6 |
| The representations of SU(3) | p. 7 |
| Dimensions of the IRs | p. 8 |
| Isospin and hypercharge | p. 9 |
| Isospin-hypercharge decompositions | p. 10 |
| The Clebsch-Gordan series | p. 12 |
| Some theorems | p. 15 |
| Invariant couplings | p. 17 |
| The problem of Cartesian components | p. 17 |
| SU(2) again | p. 18 |
| SU(3) octets: trilinear couplings | p. 19 |
| SU(3) OCTETS: QUADRILINEAR COUPLINGS | p. 20 |
| A mixed notation | p. 21 |
| Applications | p. 23 |
| Electromagnetism | p. 23 |
| Magnetic moments: baryons | p. 24 |
| Electromagnetic mass splittings | p. 25 |
| Electromagnetic properties of the decuplet | p. 26 |
| The medium-strong interactions | p. 26 |
| Ideas of octet enhancement | p. 28 |
| Bibliography | p. 35 |
| Soft pions | |
| The reduction formula | p. 36 |
| The weak interactions: first principles | p. 40 |
| The Goldberger-Treiman relation and a first glance at PCAC | p. 41 |
| A hard look at PCAC | p. 42 |
| The gradient-coupling model | p. 45 |
| Adler's rule for the emission of one soft pion | p. 47 |
| Current commutators | p. 50 |
| Vector-vector commutators | p. 50 |
| Vector-axial commutators | p. 51 |
| Axial-axial commutators | p. 51 |
| The Weinberg-Tomozawa formula and the Adler-Weisberger relation | p. 52 |
| Pion-pion scattering a la Weinberg | p. 57 |
| Kaon decays | p. 60 |
| Notational conventions | p. 63 |
| No-renormalization theorem | p. 63 |
| Threshold S-matrix and threshold scattering lengths | p. 64 |
| Bibliography | p. 65 |
| Dilatations | |
| Introduction | p. 67 |
| The formal theory of broken scale invariance | p. 68 |
| Symmetries, currents, and Ward identities | p. 68 |
| Scale transformations and scale dimensions | p. 70 |
| More about the scale current and a quick look at the conformal group | p. 71 |
| Hidden scale invariance | p. 76 |
| The death of scale invariance | p. 79 |
| Some definitions and technical details | p. 79 |
| A disaster in the deep Euclidean region | p. 80 |
| Anomalous dimensions and other anomalies | p. 82 |
| The last anomalies: the Callan-Symanzik equations | p. 84 |
| The resurrection of scale invariance | p. 88 |
| The renormalization group equations and their solution | p. 88 |
| The return of scaling in the deep Euclidean region | p. 90 |
| Scaling and the operator product expansion | p. 93 |
| Conclusions and questions | p. 96 |
| Notes and references | p. 97 |
| Renormalization and symmetry: a review for non-specialists | |
| Introduction | p. 99 |
| Bogoliubov's method and Hepp's theorem | p. 99 |
| Renormalizable and non-renormalizable interactions | p. 104 |
| Symmetry and symmetry-breaking: Symanzik's rule | p. 106 |
| Symmetry and symmetry-breaking: currents | p. 108 |
| Notes and references | p. 111 |
| Secret symmetry: an introduction to spontaneous symmetry breakdown and gauge fields | |
| Introduction | p. 113 |
| Secret symmetries in classical field theory | p. 115 |
| The idea of spontaneous symmetry breakdown | p. 115 |
| Goldstone bosons in an Abelian model | p. 118 |
| Goldstone bosons in the general case | p. 119 |
| The Higgs phenomenon in the Abelian model | p. 121 |
| Yang-Mills fields and the Higgs phenomenon in the general case | p. 124 |
| Summary and remarks | p. 126 |
| Secret renormalizability | p. 128 |
| The order of the arguments | p. 128 |
| Renormalization reviewed | p. 128 |
| Functional methods and the effective potential | p. 132 |
| The loop expansion | p. 135 |
| A sample computation | p. 136 |
| The most important part of this lecture | p. 138 |
| The physical meaning of the effective potential | p. 139 |
| Accidental symmetry and related phenomena | p. 142 |
| An alternative method of computation | p. 144 |
| Functional integration (vulgarized) | p. 145 |
| Integration over infinite-dimensional spaces | p. 145 |
| Functional integrals and generating functionals | p. 148 |
| Feynman rules | p. 152 |
| Derivative interactions | p. 154 |
| Fermi fields | p. 156 |
| Ghost fields | p. 158 |
| The Feynman rules for gauge field theories | p. 159 |
| Troubles with gauge invariance | p. 159 |
| The Faddeev-Popov Ansatz | p. 160 |
| The application of the Ansatz | p. 163 |
| Justification of the Ansatz | p. 165 |
| Concluding remarks | p. 167 |
| Asymptotic freedom | p. 169 |
| Operator products and deep inelastic electroproduction | p. 169 |
| Massless field theories and the renormalization group | p. 171 |
| Exact and approximate solutions of the renormalization group equations | p. 174 |
| Asymptotic freedom | p. 176 |
| No conclusions | p. 179 |
| One-loop effective potential in the general case | p. 180 |
| Notes and references | p. 182 |
| Classical lumps and their quantum descendants | |
| Introduction | p. 185 |
| Simple examples and their properties | p. 187 |
| Some time-independent lumps in one space dimension | p. 187 |
| Small oscillations and stability | p. 191 |
| Lumps are like particles (almost) | p. 192 |
| More dimensions and a discouraging theorem | p. 194 |
| Topological conservation laws | p. 195 |
| The basic idea and the main results | p. 195 |
| Gauge field theories revisited | p. 198 |
| Topological conservation laws, or, homotopy classes | p. 202 |
| Three examples in two spatial dimensions | p. 205 |
| Three examples in three dimensions | p. 208 |
| Patching together distant solutions, or, homotopy groups | p. 209 |
| Abelian and non-Abelian magnetic monopoles, or, [Pi][subscript 2](G/H) as a subgroup of [Pi][subscript 1](H) | p. 215 |
| Quantum lumps | p. 223 |
| The nature of the classical limit | p. 223 |
| Time-independent lumps: power-series expansion | p. 225 |
| Time-independent lumps: coherent-state variational method | p. 232 |
| Periodic lumps: the old quantum theory and the DHN formula | p. 239 |
| A very special system | p. 246 |
| A curious equivalence | p. 246 |
| The secret of the soliton | p. 250 |
| Qualitative and quantitative knowledge | p. 252 |
| Some opinions | p. 253 |
| A three-dimensional scalar theory with non-dissipative solutions | p. 254 |
| A theorem on gauge fields | p. 256 |
| A trivial extension | p. 257 |
| Looking for solutions | p. 257 |
| Singular and non-singular gauge fields | p. 259 |
| Notes and references | p. 262 |
| The uses of instantons | |
| Introduction | p. 265 |
| Instantons and bounces in particle mechanics | p. 268 |
| Euclidean functional integrals | p. 268 |
| The double well and instantons | p. 270 |
| Periodic potentials | p. 277 |
| Unstable states and bounces | p. 278 |
| The vacuum structure of gauge field theories | p. 282 |
| Old stuff | p. 282 |
| The winding number | p. 284 |
| Many vacua | p. 291 |
| Instantons: generalities | p. 295 |
| Instantons: particulars | p. 297 |
| The evaluation of the determinant and an infrared embarrassment | p. 300 |
| The Abelian Higgs model in 1 + 1 dimensions | p. 302 |
| 't Hooft's solution of the U(1) problem | p. 307 |
| The mystery of the missing meson | p. 307 |
| Preliminaries: Euclidean Fermi fields | p. 311 |
| Preliminaries: chiral Ward identities | p. 314 |
| QCD (baby version) | p. 316 |
| QCD (the real thing) | p. 323 |
| Miscellany | p. 324 |
| The fate of the false vacuum | p. 327 |
| Unstable vacua | p. 327 |
| The bounce | p. 329 |
| The thin-wall approximation | p. 332 |
| The fate of the false vacuum | p. 334 |
| Determinants and renormalization | p. 336 |
| Unanswered questions | p. 339 |
| How to compute determinants | p. 340 |
| The double well done doubly well | p. 341 |
| Finite action is zero measure | p. 344 |
| Only winding number survives | p. 345 |
| No wrong-chirality solutions | p. 347 |
| Notes and references | p. 348 |
| 1/N | |
| Introduction | p. 351 |
| Vector representations, or, soluble models | p. 352 |
| [phi][superscript 4] theory (half-way) | p. 352 |
| The Gross-Neveu model | p. 358 |
| The CP[superscript N - 1] model | p. 362 |
| Adjoint representations, or, chromodynamics | p. 368 |
| The double-line representation and the dominance of planar graphs | p. 368 |
| Topology and phenomenology | p. 373 |
| The 't Hooft model | p. 378 |
| Witten's theory of baryons | p. 386 |
| The master field | p. 391 |
| Restrospect and prospect | p. 396 |
| The Euler characteristic | p. 397 |
| The 't Hooft equations | p. 398 |
| U(N) as an approximation to SU(N) | p. 400 |
| Notes and references | p. 401 |
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