Broken Symmetry: Selected Papers of Y. Nambu (World Scientific Series in 20th Century Physics 13)

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 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 The unpublished lecture note on string theory (1969) and the first paper on spontaneous symmetry breaking (1961) are retyped and included.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 Professor Nambu on his research career. CONTENTS......Page 16 FOREWORD......Page 6 RESEARCH IN ELEMENTARY PARTICLE THEORY......Page 8 References......Page 15 § 2. Preliminary Considerations......Page 20 § 3. Onsager's Problem......Page 24 § 4. Kramers-Wannier's method of approach......Page 28 § 5. Additional Remarks......Page 31 References......Page 32 1. Introduction......Page 33 2. Formal introduction of the proper time......Page 34 3. Theory of Fock and its extension......Page 37 4. Problem of vacuum polarization......Page 40 Appendix. Solution for an arbitrary constant external field......Page 43 References......Page 45 1. Introduction and Summary......Page 46 2. The Second Order Potential......Page 47 3. The Fourth Order Potential......Page 54 4. The Relation between the Second and Fourth Order Potential......Page 59 5. Further Discussions......Page 61 References......Page 65 On the Nature of V-Particles, I......Page 66 Appendix......Page 69 On the Nature of V-Particles, II......Page 70 References......Page 72 POSSIBLE EXISTENCE OF A HEAVY NEUTRAL MESON......Page 74 1. Introduction......Page 76 2. Derivation of the representation......Page 77 3. Application to the three-field Green's function......Page 87 4. Remarks......Page 90 APPENDIX I......Page 91 APPENDIX II......Page 92 RIASSUNTO......Page 95 1. Introduction......Page 96 2. Representoation of the nucleon form factors......Page 98 3. A theorem about the final state interaction......Page 101 4. Form factors in a more general case......Page 103 5. Concluding remarks......Page 106 Representation for generalized form factors......Page 107 Proof of the Theorem in Sect. 4......Page 108 RIASSUNTO......Page 109 1. INTRODUCTION......Page 110 2. FEYNMAN-DYSON FORMULATION......Page 112 3. NONLOCAL (ENERGY-DEPENDENT) SELF-CONSISTENCY CONDITIONS......Page 115 4. INTEGRAL EQUATIONS FOR VERTEX PARTS......Page 117 5. GAUGE INVARIANCE IN THE MEISSNER EFFECT......Page 119 6. THE COLLECTIVE EXCITATIONS......Page 120 7. CALCULATION OF THE CHARGE-CURRENT VERTEX FUNCTIONS......Page 122 8. THE PLASMA OSCILLATIONS......Page 123 9. CONCLUDING REMARKS......Page 124 ACKNOWLEDGMENT......Page 125 AXIAL VECTOR CURRENT CONSERVATION IN WEAK INTERACTIONS......Page 126 A 'SUPERCONDUCTOR' MODEL OF ELEMENTARY PARTICLES AND ITS CONSEQUENCES......Page 129 References......Page 143 DISCUSSION......Page 144 I. INTRODUCTION......Page 146 II. THE PRIMARY INTERACTION......Page 148 III. THE SELF-CONSISTENT EQUATION FOR NUCLEON MASS......Page 149 IV. THE COLLECTIVE STATES......Page 152 V. PHENOMENOLOGICAL THEORY AND γ5 INVARIANCE......Page 155 VI. THE CONSERVATION OF AXIAL VECTOR CURRENT......Page 157 VII. SUMMARY AND DISCUSSION......Page 158 APPENDIX......Page 159 II. MODEL LAGRANGIAN FOR THE NUCLEON......Page 160 A. Pseudoscalar, Isovector Meson......Page 161 IV. VIOLATION OF γ5, INVARIANCE......Page 162 V. IMPLICATIONS OF THE MODEL......Page 164 VI. FURTHER PROBLEM......Page 166 APPENDIX......Page 168 II. THE NISHIJIMA MODEL......Page 169 III. PERTURBATION CALCULATION......Page 171 IV. GENERAL PROOF......Page 172 V. γ5x ISOSPIN INVARIANCE AND THE EXPERIMENTAL TEST......Page 173 VI. FURTHER REMARKS......Page 175 ACKNOWLEDGMENTS......Page 176 1. INTRODUCTION......Page 177 2. DIAGRAMMATIC INTERPRETATION OF THE FORMULA......Page 178 4. ELECTROPION PRODUCTION......Page 179 5. CALCULATION OF CROSS SECTION......Page 181 6. NEUTRINO-PION PRODUCTIONS......Page 182 2. GENERAL FORMULATION......Page 184 3. CALCULATIONS......Page 186 4. PROOF OF GAUGE INVARIANCE......Page 189 5. RELATION TO THE SIMPLE VARIATIONAL METHOD......Page 190 ACKNOWLEDGMENTS......Page 191 1. INTRODUCTION......Page 192 2. THE DISCRETE QUANTIZATION MODEL......Page 193 3. PERTURBATION CALCULATION IN THIN FILMS......Page 197 4. EXTENSION OF THE PERTURBATION FORMULA......Page 199 5. PHASE TRANSITION AT FINITE TEMPERATURES......Page 201 7. COMPARISON WITH OTHER THEORIES......Page 203 8. CONCLUDING REMARKS......Page 204 ACKNOWLEDGMENTS......Page 205 I. INTRODUCTION......Page 206 II. THREE TRIPLETS......Page 207 III. DOUBLE SU(3) SYMMETRY......Page 208 ACKNOWLEDGMENTS......Page 210 A SYSTEMATICS OF HADRONS IN SUBNUCLEAR PHYSICS......Page 211 REFERENCES......Page 220 NONLEPTONIC DECAYS OF HYPERONS......Page 221 §1. Introduction......Page 225 §2. General structure of wave equations and the use of operator method......Page 228 §3. An infinitely coupled equation based on non-unitary representations......Page 231 §4. An example based on a unitary representation......Page 235 Summary and discussion......Page 238 References......Page 239 I. Introduction......Page 240 II. Choice of the dynamical group G and its representation......Page 243 III. Models based on SL(2,c)......Page 244 1. Form factors......Page 245 2. Wave equations......Page 246 3. Minimal electromagnetic interaction......Page 247 IV. Models based on SO(4, 2)~SU(2, 2)......Page 248 V. Models based on SU(3,1)......Page 251 VI. Problems of quantized fields......Page 252 VII. Scattering processes......Page 254 VIII. Application to hadron physics......Page 256 References......Page 258 Discussion......Page 260 Quantum Electrodynamics in Nonlinear Gauge......Page 267 Note added in proof......Page 272 S-MATRIX IN SEMICLASSICAL APPROXIMATION......Page 273 Quark model and the factorization of the Veneziano amplitude......Page 277 References......Page 285 DISCUSSION......Page 286 1. Introduction......Page 287 2. Spontaneous breakdown of symmetries......Page 288 3. PCAC, Current Algebra, and Soft Pion......Page 291 4. Unified description of hadron symmetries......Page 294 5. Further search for spontaneous breakdown......Page 295 FOOTNOTES......Page 296 Duality and Hadrodynamics......Page 299 1 Introduction......Page 300 2 Factorized Veneziano model......Page 302 3 Quarks and the dual model......Page 308 4 Statistical approximation......Page 314 5 Electromagnetic interactions and inelastic e - p scattering......Page 316 I. INTRODUCTION......Page 321 II. CANONICAL TRANSFORMATION......Page 322 III. QUANTIZATION......Page 324 IV. USE OF NONASSOCIATIVE ALGEBRAS......Page 326 V. SUMMARY......Page 327 I. INTRODUCTION......Page 329 II. MODIFIED DIRAC MONOPOLE THEORY......Page 330 III. QUANTIZATION......Page 332 IV. IMPLICATIONS FOR HADRON PHYSICS......Page 333 I. RELATIVISTIC HYDRODYNAMICS OF VORTICES......Page 336 A. Massive 6-Vector Field......Page 340 B. Confinement with Nonlocal Fields......Page 341 C. Non-Abelian Analogs......Page 342 III. ALGEBRAIC CHARACTERIZATION OF STRING AND GAUGE FIELD EQUATIONS......Page 343 ADDENDUM......Page 347 1. Introduction......Page 348 2. General formalism for dealing with monopoles and strings......Page 350 3. String-monopole solution in a SU(2) × U(1) model......Page 351 4. Dynamics of a rotating dumb bell......Page 355 5. Discussion......Page 357 References......Page 358 HAMILTON-JACOBI FORMALISM FOR STRINGS......Page 359 References......Page 362 1. The paradigms of particle physics......Page 363 1. Model building in terms of particles......Page 364 2. Renormalization theory......Page 365 3. Symmetries and symmetry breaking......Page 366 4. The gauge principle......Page 367 2. Problems and issues......Page 369 1. General questions on quantum mechanics......Page 370 2. Limits of renormalizable field theory......Page 371 (a) Lattice theories......Page 372 (b) Topological excitations......Page 373 (c) Chiral anomaly and relative phenomena......Page 375 3. Quantum mechanics of extended objects......Page 376 4. Supersymmetry......Page 377 (a) Supersymmetric oscillator and Wigner-Yang oscillator......Page 378 (c) Quasi-supersymmetry in nonrelativistic phenomena......Page 379 3. Speculative outlook......Page 380 2. Broken symmetries......Page 381 References......Page 382 2. Superconductivity......Page 385 3. Helium 3......Page 386 4. Nuclear physics......Page 387 References......Page 389 1 INTRODUCTION......Page 390 2 MATHEMATICAL PRELIMINARIES......Page 391 3 HEAT EQUATION......Page 393 4 THE WAVE EQUATION......Page 397 5.1 Higher dimensional wave equations......Page 398 5.2 Partition function......Page 400 REFERENCES......Page 401 § 1. Modes of quest in particle physics......Page 402 § 2. Evolution of the Lawrence-Yukawa paradigm......Page 403 § 3. The rise of the Dirac mode......Page 404 § 4. Speculative comments......Page 405 References......Page 408 1. Introduction......Page 409 2. Fermionic operators in superconductivity......Page 410 3. General forms of fermion operators......Page 412 4. Comments......Page 415 References......Page 417 ABSTRACT......Page 418 References......Page 424 1. INTRODUCTION......Page 425 2. BASIC FEATURES OF THE BCS THEORY......Page 426 3. RELATIVISTIC QUASI-SUPERSYMMETRY......Page 427 4. BOOTSTRAP SYMMETRY BREAKING......Page 429 REFERENCES......Page 432 1. INTRODUCTION......Page 435 2. MODES AND MASSES IN BCS......Page 437 3. BCS IN THE NUCLEUS......Page 441 4. BOSONIC INTERACTIONS......Page 443 5. FINITENESS......Page 445 6. FERMIONS AND SUPERSYMMETRY......Page 447 7. THE SU(3) CHAIN......Page 450 8. CONCLUSIONS AND SPECULATIONS......Page 452 ACKNOWLEDGMENTS......Page 453 REFERENCES......Page 454 1. Introduction......Page 455 2. Symmetry and Symmetry Breaking......Page 456 3. Dynamical (Spontaneous ) Symmetry Breaking......Page 458 4. The BCS Mechanism......Page 462 5. Tumbling and Bootstrap......Page 464 REFERENCES......Page 469 Positions......Page 472 Honors......Page 473 List of Publications......Page 474 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.