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| Preface | |
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| Acknowledgements | |
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| An introduction to unitary symmetry | |
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| The search for higher symmetries | |
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| The eight-baryon puzzle | |
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| The elimination of G[subscript 0] | |
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| SU(3) and its representations | |
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| The representations of SU(n) | |
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| The representations of SU(2) | |
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| The representations of SU(3) | |
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| Dimensions of the IRs | |
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| Isospin and hypercharge | |
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| Isospin-hypercharge decompositions | |
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| The Clebsch-Gordan series | |
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| Some theorems | |
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| Invariant couplings | |
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| The problem of Cartesian components | |
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| SU(2) again | |
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| SU(3) octets: trilinear couplings | |
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| SU(3) OCTETS: QUADRILINEAR COUPLINGS | |
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| A mixed notation | |
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| Applications | |
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| Electromagnetism | |
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| Magnetic moments: baryons | |
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| Electromagnetic mass splittings | |
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| Electromagnetic properties of the decuplet | |
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| The medium-strong interactions | |
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| Ideas of octet enhancement | |
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| Bibliography | |
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| Soft pions | |
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| The reduction formula | |
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| The weak interactions: first principles | |
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| The Goldberger-Treiman relation and a first glance at PCAC | |
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| A hard look at PCAC | |
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| The gradient-coupling model | |
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| Adler's rule for the emission of one soft pion | |
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| Current commutators | |
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| Vector-vector commutators | |
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| Vector-axial commutators | |
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| Axial-axial commutators | |
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| The Weinberg-Tomozawa formula and the Adler-Weisberger relation | |
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| Pion-pion scattering a la Weinberg | |
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| Kaon decays | |
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| Notational conventions | |
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| No-renormalization theorem | |
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| Threshold S-matrix and threshold scattering lengths | |
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| Bibliography | |
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| Dilatations | |
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| Introduction | |
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| The formal theory of broken scale invariance | |
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| Symmetries, currents, and Ward identities | |
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| Scale transformations and scale dimensions | |
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| More about the scale current and a quick look at the conformal group | |
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| Hidden scale invariance | |
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| The death of scale invariance | |
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| Some definitions and technical details | |
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| A disaster in the deep Euclidean region | |
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| Anomalous dimensions and other anomalies | |
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| The last anomalies: the Callan-Symanzik equations | |
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| The resurrection of scale invariance | |
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| The renormalization group equations and their solution | |
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| The return of scaling in the deep Euclidean region | |
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| Scaling and the operator product expansion | |
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| Conclusions and questions | |
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| Notes and references | |
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| Renormalization and symmetry: a review for non-specialists | |
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| Introduction | |
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| Bogoliubov's method and Hepp's theorem | |
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| Renormalizable and non-renormalizable interactions | |
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| Symmetry and symmetry-breaking: Symanzik's rule | |
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| Symmetry and symmetry-breaking: currents | |
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| Notes and references | |
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| Secret symmetry: an introduction to spontaneous symmetry breakdown and gauge fields | |
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| Introduction | |
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| Secret symmetries in classical field theory | |
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| The idea of spontaneous symmetry breakdown | |
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| Goldstone bosons in an Abelian model | |
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| Goldstone bosons in the general case | |
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| The Higgs phenomenon in the Abelian model | |
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| Yang-Mills fields and the Higgs phenomenon in the general case | |
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| Summary and remarks | |
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| Secret renormalizability | |
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| The order of the arguments | |
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| Renormalization reviewed | |
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| Functional methods and the effective potential | |
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| The loop expansion | |
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| A sample computation | |
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| The most important part of this lecture | |
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| The physical meaning of the effective potential | |
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| Accidental symmetry and related phenomena | |
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| An alternative method of computation | |
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| Functional integration (vulgarized) | |
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| Integration over infinite-dimensional spaces | |
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| Functional integrals and generating functionals | |
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| Feynman rules | |
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| Derivative interactions | |
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| Fermi fields | |
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| Ghost fields | |
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| The Feynman rules for gauge field theories | |
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| Troubles with gauge invariance | |
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| The Faddeev-Popov Ansatz | |
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| The application of the Ansatz | |
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| Justification of the Ansatz | |
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| Concluding remarks | |
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| Asymptotic freedom | |
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| Operator products and deep inelastic electroproduction | |
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| Massless field theories and the renormalization group | |
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| Exact and approximate solutions of the renormalization group equations | |
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| Asymptotic freedom | |
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| No conclusions | |
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| One-loop effective potential in the general case | |
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| Notes and references | |
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| Classical lumps and their quantum descendants | |
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| Introduction | |
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| Simple examples and their properties | |
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| Some time-independent lumps in one space dimension | |
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| Small oscillations and stability | |
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| Lumps are like particles (almost) | |
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| More dimensions and a discouraging theorem | |
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| Topological conservation laws | |
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| The basic idea and the main results | |
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| Gauge field theories revisited | |
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| Topological conservation laws, or, homotopy classes | |
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| Three examples in two spatial dimensions | |
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| Three examples in three dimensions | |
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| Patching together distant solutions, or, homotopy groups | |
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| Abelian and non-Abelian magnetic monopoles, or, [Pi][subscript 2](G/H) as a subgroup of [Pi][subscript 1](H) | |
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| Quantum lumps | |
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| The nature of the classical limit | |
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| Time-independent lumps: power-series expansion | |
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| Time-independent lumps: coherent-state variational method | |
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| Periodic lumps: the old quantum theory and the DHN formula | |
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| A very special system | |
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| A curious equivalence | |
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| The secret of the soliton | |
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| Qualitative and quantitative knowledge | |
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| Some opinions | |
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| A three-dimensional scalar theory with non-dissipative solutions | |
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| A theorem on gauge fields | |
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| A trivial extension | |
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| Looking for solutions | |
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| Singular and non-singular gauge fields | |
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| Notes and references | |
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| The uses of instantons | |
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| Introduction | |
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| Instantons and bounces in particle mechanics | |
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| Euclidean functional integrals | |
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| The double well and instantons | |
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| Periodic potentials | |
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| Unstable states and bounces | |
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| The vacuum structure of gauge field theories | |
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| Old stuff | |
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| The winding number | |
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| Many vacua | |
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| Instantons: generalities | |
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| Instantons: particulars | |
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| The evaluation of the determinant and an infrared embarrassment | |
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| The Abelian Higgs model in 1 + 1 dimensions | |
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| 't Hooft's solution of the U(1) problem | |
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| The mystery of the missing meson | |
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| Preliminaries: Euclidean Fermi fields | |
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| Preliminaries: chiral Ward identities | |
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| QCD (baby version) | |
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| QCD (the real thing) | |
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| Miscellany | |
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| The fate of the false vacuum | |
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| Unstable vacua | |
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| The bounce | |
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| The thin-wall approximation | |
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| The fate of the false vacuum | |
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| Determinants and renormalization | |
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| Unanswered questions | |
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| How to compute determinants | |
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| The double well done doubly well | |
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| Finite action is zero measure | |
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| Only winding number survives | |
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| No wrong-chirality solutions | |
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| Notes and references | |
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| 1/N | |
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| Introduction | |
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| Vector representations, or, soluble models | |
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| [phi][superscript 4] theory (half-way) | |
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| The Gross-Neveu model | |
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| The CP[superscript N - 1] model | |
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| Adjoint representations, or, chromodynamics | |
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| The double-line representation and the dominance of planar graphs | |
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| Topology and phenomenology | |
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| The 't Hooft model | |
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| Witten's theory of baryons | |
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| The master field | |
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| Restrospect and prospect | |
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| The Euler characteristic | |
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| The 't Hooft equations | |
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| U(N) as an approximation to SU(N) | |
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| Notes and references | |