Broken Symmetry: Selected Papers of Y Nambu (Advanced Series in Electrical and Computer Engineering)

This book contains selected papers of Prof Nambu who is one of the most original and outstanding particle theorists of our time. This volume consists of about 40 papers which made fundamental contributions to our understanding of particle physics during the last few decades.The unpublished lecture note on string theory (1969) and the first paper on spontaneous symmetry breaking (1961) are retyped and included. The book also contains a memoir of Prof Nambu on his research career. CONTENTS FOREWORD RESEARCH IN ELEMENTARY PARTICLE THEORY References A Note on the Eigenvalue Problem in Crystal Statistics § 1. Introduction § 2. Preliminary Considerations § 3. Onsager's Problem § 4. Kramers-Wannier's method of approach § 5. Additional Remarks References The Use of the Proper Time in Quantum Electrodynamics I 1. Introduction 2. Formal introduction of the proper time 3. Theory of Fock and its extension 4. Problem of vacuum polarization Appendix. Solution for an arbitrary constant external field References Force Potentials in Quantum Field Theory 1. Introduction and Summary 2. The Second Order Potential 3. The Fourth Order Potential 4. The Relation between the Second and Fourth Order Potential 5. Further Discussions References On the Nature of V-Particles, I Appendix On the Nature of V-Particles, II References POSSIBLE EXISTENCE OF A HEAVY NEUTRAL MESON Parametric Representations of General Green's Functions Summary 1. Introduction 2. Derivation of the representation 3. Application to the three-field Green's function 4. Remarks APPENDIX I APPENDIX II RIASSUNTO Dispersion Relations for Form Factors Summary 1. Introduction 2. Representoation of the nucleon form factors 3. A theorem about the final state interaction 4. Form factors in a more general case 5. Concluding remarks APPENDIX I Representation for generalized form factors APPENDIX II Proof of the Theorem in Sect. 4 RIASSUNTO Quasi-Particles and Gauge Invariance in the Theory of Superconductivity 1. INTRODUCTION 2. FEYNMAN-DYSON FORMULATION 3. NONLOCAL (ENERGY-DEPENDENT) SELF-CONSISTENCY CONDITIONS 4. INTEGRAL EQUATIONS FOR VERTEX PARTS 5. GAUGE INVARIANCE IN THE MEISSNER EFFECT 6. THE COLLECTIVE EXCITATIONS 7. CALCULATION OF THE CHARGE-CURRENT VERTEX FUNCTIONS 8. THE PLASMA OSCILLATIONS 9. CONCLUDING REMARKS ACKNOWLEDGMENT AXIAL VECTOR CURRENT CONSERVATION IN WEAK INTERACTIONS A 'SUPERCONDUCTOR' MODEL OF ELEMENTARY PARTICLES AND ITS CONSEQUENCES References DISCUSSION Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. I I. INTRODUCTION II. THE PRIMARY INTERACTION III. THE SELF-CONSISTENT EQUATION FOR NUCLEON MASS IV. THE COLLECTIVE STATES VI. THE CONSERVATION OF AXIAL VECTOR CURRENT VII. SUMMARY AND DISCUSSION APPENDIX Dynamical Model of Elementary Particles Based on an Analogy with Superconductivity. II I. INTRODUCTION II. MODEL LAGRANGIAN FOR THE NUCLEON III. DETERMINATION OF MESON STATES A. Pseudoscalar, Isovector Meson B. Scalar, Isoscalar Meson C. Vector Mesons D. The "Deuteron" States V. IMPLICATIONS OF THE MODEL VI. FURTHER PROBLEM APPENDIX Chirality Conservation and Soft Pion Production I. INTRODUCTION II. THE NISHIJIMA MODEL III. PERTURBATION CALCULATION IV. GENERAL PROOF VI. FURTHER REMARKS ACKNOWLEDGMENTS Soft Pion Emission Induced by Electromagnetic and Weak Interactions 1. INTRODUCTION 2. DIAGRAMMATIC INTERPRETATION OF THE FORMULA 3. REACTIONS INDUCED BY CHIRALITY NONCONSERVING PERTURBATIONS 4. ELECTROPION PRODUCTION 5. CALCULATION OF CROSS SECTION 6. NEUTRINO-PION PRODUCTIONS Magnetic Field Dependence of the Energy Gap in Superconductors 1. INTRODUCTION 2. GENERAL FORMULATION 3. CALCULATIONS 4. PROOF OF GAUGE INVARIANCE 5. RELATION TO THE SIMPLE VARIATIONAL METHOD CONCLUDING REMARKS ACKNOWLEDGMENTS Considerations on the Magnetic Field Problem in Superconducting Thin Films 1. INTRODUCTION 2. THE DISCRETE QUANTIZATION MODEL 3. PERTURBATION CALCULATION IN THIN FILMS 4. EXTENSION OF THE PERTURBATION FORMULA 5. PHASE TRANSITION AT FINITE TEMPERATURES 6. COMPARISON BETWEEN THEORY AND EXPERIMENT 7. COMPARISON WITH OTHER THEORIES 8. CONCLUDING REMARKS ACKNOWLEDGMENTS Three-Triplet Model with Double SU(3) Symmetry I. INTRODUCTION II. THREE TRIPLETS III. DOUBLE SU(3) SYMMETRY ACKNOWLEDGMENTS A SYSTEMATICS OF HADRONS IN SUBNUCLEAR PHYSICS REFERENCES NONLEPTONIC DECAYS OF HYPERONS Relativistic Wave Equations for Particles with Internal Structure and Mass Spectrum §1. Introduction §2. General structure of wave equations and the use of operator method §3. An infinitely coupled equation based on non-unitary representations §4. An example based on a unitary representation Summary and discussion References Infinite Multiplets I. Introduction II. Choice of the dynamical group G and its representation III. Models based on SL(2,c) 1. Form factors 2. Wave equations 3. Minimal electromagnetic interaction IV. Models based on SO(4, 2)~SU(2, 2) V. Models based on SU(3,1) VI. Problems of quantized fields VII. Scattering processes VIII. Application to hadron physics References Discussion Quantum Electrodynamics in Nonlinear Gauge References Note added in proof S-MATRIX IN SEMICLASSICAL APPROXIMATION Quark model and the factorization of the Veneziano amplitude References DISCUSSION SYMMETRY BREAKDOWN AND SMALL MASS BOSONS 1. Introduction 2. Spontaneous breakdown of symmetries 3. PCAC, Current Algebra, and Soft Pion 4. Unified description of hadron symmetries 5. Further search for spontaneous breakdown FOOTNOTES Duality and Hadrodynamics 1 Introduction 2 Factorized Veneziano model 3 Quarks and the dual model 4 Statistical approximation 5 Electromagnetic interactions and inelastic e - p scattering Generalized Hamiltonian Dynamics I. INTRODUCTION II. CANONICAL TRANSFORMATION III. QUANTIZATION IV. USE OF NONASSOCIATIVE ALGEBRAS V. SUMMARY Strings, monopoles, and gauge fields I. INTRODUCTION II. MODIFIED DIRAC MONOPOLE THEORY III. QUANTIZATION IV. IMPLICATIONS FOR HADRON PHYSICS Strings, Vortices, and Gauge Fields I. RELATIVISTIC HYDRODYNAMICS OF VORTICES II. BROKEN SYMMETRY SCHEMES AND OTHER GENERALIZATIONS A. Massive 6-Vector Field B. Confinement with Nonlocal Fields C. Non-Abelian Analogs III. ALGEBRAIC CHARACTERIZATION OF STRING AND GAUGE FIELD EQUATIONS REFERENCES ADDENDUM STRING-LIKE CONFIGURATIONS IN THE WEINBERG-SALAM THEORY 1. Introduction 2. General formalism for dealing with monopoles and strings 3. String-monopole solution in a SU(2) × U(1) model 4. Dynamics of a rotating dumb bell 5. Discussion References HAMILTON-JACOBI FORMALISM FOR STRINGS References Concluding Remarks 1. The paradigms of particle physics 1. Model building in terms of particles 2. Renormalization theory 3. Symmetries and symmetry breaking 4. The gauge principle 2. Problems and issues 1. General questions on quantum mechanics 2. Limits of renormalizable field theory (a) Lattice theories (b) Topological excitations (c) Chiral anomaly and relative phenomena 3. Quantum mechanics of extended objects 4. Supersymmetry (a) Supersymmetric oscillator and Wigner-Yang oscillator (b) Fermionic zero modes associated with topological excitations (c) Quasi-supersymmetry in nonrelativistic phenomena 3. Speculative outlook 1. Mass and mass spectra 2. Broken symmetries 3. Phenomenology of grand unification 4. Beyond the Planck limit References FERMION-BOSON RELATIONS IN BCS-TYPE THEORIES 1. Introduction 2. Superconductivity 3. Helium 3 4. Nuclear physics 5. Particle physics Acknowledgements References Field Theory of Galois' Fields 1 INTRODUCTION 2 MATHEMATICAL PRELIMINARIES 3 HEAT EQUATION 4 THE WAVE EQUATION 5 OTHER PROBLEMS 5.1 Higher dimensional wave equations 5.2 Partition function ACKNOWLEDGMENTS REFERENCES Directions of Particle Physics § 1. Modes of quest in particle physics § 2. Evolution of the Lawrence-Yukawa paradigm § 3. The rise of the Dirac mode § 4. Speculative comments References Supersymmetry and Superconductivity ABSTRACT 1. Introduction 2. Fermionic operators in superconductivity 3. General forms of fermion operators 4. Comments References THERMODYNAMIC ANALOGY IN QUANTUM FIELD THEORY ABSTRACT References BCS MECHANISM, QUASI-SUPERSYMMETRY, AND FERMION MASSES ABSTRACT 1. INTRODUCTION 2. BASIC FEATURES OF THE BCS THEORY 3. RELATIVISTIC QUASI-SUPERSYMMETRY 4. BOOTSTRAP SYMMETRY BREAKING REFERENCES BCS and IBM 1. INTRODUCTION 2. MODES AND MASSES IN BCS 3. BCS IN THE NUCLEUS 4. BOSONIC INTERACTIONS 5. FINITENESS 6. FERMIONS AND SUPERSYMMETRY 7. THE SU(3) CHAIN 8. CONCLUSIONS AND SPECULATIONS ACKNOWLEDGMENTS REFERENCES Dynamical Symmetry Breaking ABSTRACT 1. Introduction 2. Symmetry and Symmetry Breaking 3. Dynamical (Spontaneous ) Symmetry Breaking 4. The BCS Mechanism 5. Tumbling and Bootstrap REFERENCES YOICHIRO NAMBU Education Positions Honors List of Publications This text contains selected papers of the particle theorist, Professor Nambu. It comprises about 40 papers which made fundamental contributions to our understanding of particle physics.