Contents About the Authors Preface to the Second Edition Preface to the First Edition Chapter 1. Overview 1 References 7 Chapter 2. Symmetry and Conservation Law 9 2.1 Introduction 9 2.2 The Action, Equation of Motion and Conserved Quantities 10 2.3 Parity Transformation 14 2.3.1 Klein-Gordon field *(x) 15 2.3.2 Parity transformation of fermion field 16 2.3.3 Parity transformation of vector field 18 2.4 Charge Conjugation 19 2.4.1 Charge conjugation of scalar field 19 2.4.2 Charge conjugation of fermion field *(x) 19 2.4.3 Charge conjugation of vector field A*{x) 22 2.5 Application: Furry Theorem — A Particle of Spin 1 Cannot Decay to 27 22 2.5.1 Furry theorem 22 2.5.2 Particles of spin 1 cannot decay into two photons 23 2.6 Time Reversal 25 2.6.1 Time reversal of Klein-Gordon field *(x) 29 2.6.2 Time reversal of fermion field 29 2.6.3 Time reversal of electromagnetic field A* (x) 30 2.7 CPT Theorem 33 References 34 Chapter 3. The Classification and Properties of Particles: Lepton and Hadrons 37 3.1 Four Types of Interactions 37 3.2 Lepton and Lepton Number Conservation 40 3.2.1 Electron, muon and neutrino 40 3.2.2 * and its neutrino v* 43 3.2.3 Helicity of neutrinos 44 3.2.4 Lepton number conservation 46 3.3 Hadrons: Conservation of Baryon Numbers 47 3.3.1 π meson 48 3.3.2 Nucleon, antinucleon and baryon number conservation 52 3.3.3 Strange particles 53 3.3.4 Resonance 57 3.4 Scattering Cross Section, Particle Lifetime and Decay Width 63 3.4.1 Scattering cross section 63 3.4.2 Particle lifetime and decay width 67 3.5 Kinematics of Particle Decay 68 3.5.1 Two-body decay 68 3.5.2 Three-body decay, Dalitz diagram 69 References 73 Chapter 4. Isospin and G Parity 75 4.1 Isospin 75 4.1.1 The concept of isospin 75 4.1.2 Isospin transformation 78 4.1.3 The law of isospin conservation in strong interaction 83 4.1.4 The isospin of mesons and baryons 84 4.1.5 An example of isospin analysis of physical processes 88 4.2 Exchange Symmetry: Generalized Identity Principle 90 4.3 Isospin Violation 92 4.4 G Parity 93 References 97 Chapter 5. Quark Model of Hadrons 99 5.1 Mathematical Basics 100 5.1.1 Decomposition of SU(n) group representation product, Young tableau 100 5.1.2 ensor analysis of the SU(3) group 104 5.1.3 SU(3) group generators and Casmir operators 107 5.2 SU(3) Quark Model, the SU(3) Flavor Wave Functions for Mesons and Baxyons 109 5.2.1 The flavor wave functions for the pseudoscalar meson octet and singlet 111 5.2.2 Flavor wave functions for the vector meson octet and singlet 114 5.2.3 Flavor wave functions for baryon octet and decuplet 115 5.3 Color Degree of Freedom 122 5.3.1 The relationship of baryon spin and statistics 123 5.3.2 π°*rr 123 5.3.3 Measurement of R value in e+e- annihilation process 124 5.4 Mass Formula of Hadrons 127 5.5 Mixing of Meson Singlet and Octet 129 5.6 OZI Rule 134 5.7 SU(6) Symmetry 135 5.8 Orbital Excitation States and Radial Excitation States,Multi-quark States and Exotic States 137 5.8.1 Orbital and radial excitation states 137 5.8.2 Multi-quark states and exotic states 138 5.9 The Discovery of c,b,t Quarks 139 5.10 Quark Confinement 140 References 141 Chapter 6. Electromagnetic Interaction 143 6.1 QED and Its Feynman Rule 144 6.2 M0ller Scattering 149 6.3 Bhabha Scattering 154 6.4 The Electromagnetic Form Factors of Nucleons 156 6.4.1 Electron-proton elastic scattering assuming proton being a point particle 157 6.4.2 Elastic scattering of electron-proton 159 6.5 Inelastic Scattering of Electron-Proton 166 6.5.1 Structure function of inelastic scattering 166 6.5.2 The structure function applied to elastic scattering 169 6.6 The Parton Model for Nucleons 171 6.7 The Unification of Parton and Quark Model 174 References 177 Chapter 7. Weak Interactions 179 7.1 Looking Back to History 179 7.2 Classification of Weak Decays 181 7.3 Nuclear β Decay 183 7.4 The Discovery of Parity Violation 185 7.4.1 *-θ Puzzle 185 7.4.2 Parity violation in β decays of cobalt 60 nuclei 186 7.5 The V-A Theory of Weak Interactions 187 7.5.1 Pure leptonic decay 187 7.5.2 Semi-leptonic decay 189 7.6 Cabibbo Theory and GIM Mechanism 191 7.7 Kobayashi-Maskawa Model 194 7.8 The Limitation of the Four Fermion Point-like Interactions and the Intermediate Vector Bosons 196 7.9 Conservation of Vector Current 198 7.10 Chiral Symmetry Breaking and PC AC 201 7.11 Mixing of Neutral Mesons and CP Violation 205 7.11.1 Quantum mechanical description 205 7.11.2 K°-*°mixing and CP violation 212 7.11.3 B°-*°mixing and CP violation 224 7.11.4 D°-*°mixing and CP violation 238 References 243 Chapter 8. Gauge Theory of Electroweak Unification 247 8.1 The Higgs Mechanism 248 8.2 Yang-Mills Theory 253 8.3 Glashow-Weinberg-Salam Electroweak Unification Model 259 8.4 The Vacuum Spontaneous Symmetry Breaking:The Higgs Mechanism 268 8.4.1 The kinetic energy, mass and self-interaction term of scalar field 272 8.4.2 The mass term of gauge field 274 8.4.3 The interaction term of the scalar and gauge fields 278 8.5 The Gain of the Fermion Mass: Yukawa Coupling 279 8.6 The Interaction of Fermion and Gauge Field II 285 8.7 The Interaction of Gauge Fields 288 8.8 Feynman Rule in the Renormalization Gauge(R* Gauge) 294 8.8.1 For pure scalar field 295 8.8.2 For the interaction of scalar and gauge fields 295 8.8.3 For ghost fields 298 8.8.4 The kinetic energy term of the Lagrangian in gauge 302 8.8.5 The interaction terms of scalar and fermions 303 8.9 The Discovery of Higgs Boson 310 References 314 Chapter 9. Theory of Strong Interaction: QCD 315 9.1 The SU(3) Gauge Symmetry of Color 316 9.2 The Quantization of Gauge Field and Fermion Field 320 9.2.1 The path integral quantization 320 9.2.2 Reduction formula 328 9.2.3 The quantization of gauge field 331 9.2.4 The quantization of fermion field and Grassmann algebra 336 9.3 The Effective Lagrangian of QCD and Perturbation Theory 342 9.3.1 The effective Lagrangian of QCD 342 9.3.2 Perturbation expansion 344 9.4 Divergence and Regularization of Loop Corrections 356 9.5 The Renormalization of Divergence 367 9.5.1 The superficial degree of divergence 368 9.5.2 The renormalizability of a theory 371 9.5.3 The renormalization of QCD 375 9.5.4 One-loop result of the renormalization constants 385 9.6 BUST Symmetry and the Generalized Ward-Takahashi Identity 391 9.6.1 BRST symmetry 391 9.6.2 The generalized Ward-Takahashi identity(Slavnov-Taylor identity) 395 9.7 The Renormalization Group Equation andthe Solution 401 9.7.1 The renormalization group 401 9.7.2 The renormalization group equations 409 9.7.3 The solution of the renormalization group equation 413 9.8 Asymptotic Freedom 416 9.9 Structure Function, Parton Distribution Function and the Application in Perturbative QCD 424 9.9.1 Structural function of deep inelastic scattering process 424 9.9.2 The prediction of QCD to the variation of structurefunction with Q2 427 9.9.3 Examples for application 429 9.10 A Brief Introduction to Some Bound States in QCD 432 9.10.1 e+e-collision, charmonium and Bottomonium 432 9.10.2 Glueball and hybrid state 434 9.11 Nonperturbative QCD and Lattice Gauge Theory 437 9.12 The Strong CP Problem 439 References 451 Chapter 10. Neutrino Oscillation 455 10.1 Experimental Evidence for Neutrino Oscillation 457 10.1.1 Atmospheric neutrino oscillation 457 10.1.2 Accelerator neutrino oscillation 459 10.1.3 Solar neutrino oscillation 460 10.1.4 Reactor neutrino oscillation 462 10.2 Theoretical Description of Neutrino Oscillation 464 10.2.1 Neutrino oscillation in vacuum 464 10.2.2 Neutrino oscillation in matter 468 10.3 Dirac Neutrino and Majorana Neutrino 472 10.3.1 Dirac neutrino 472 10.3.2 Majorana neutrino 474 10.4 Neutrino Mass and See-Saw Mechanism 476 10.5 Parameterization of Neutrino Mixing Matrix 480 10.6 CP Violation in Neutrino Oscillation 481 10.7 Neutrino Mass Hierarchy Problem 482 10.8 Perspectives 484 References 486 Chapter 11.Beyond Standard Model 489 11.1 Grand Unified Theories for Strong, Electromagnetic and Weak Interactions 490 11.1.1 SU(5) grand unified theory 490 11.1.2 SO(2N) grand unified models 509 11.1.3 Flavor unification 509 11.2 Supersymmetric Models 510 11.2.1 Superspace and superfields 513 11.2.2 Global supersymmetry and local supersymmetry(Supergravity) 514 11.2.3 Global supersymmetric theory and minimal supersymmetric standard model 515 11.3 Superstring Theory and Brane Theory 526 References 527 Chapter 12. Particle Physics and Cosmology 529 12.1 Basics of the Big Bang ACDM Model 530 12.1.1 Hubble’s law 531 12.1.2 The Robertson-Walker metric and the Friedmann equation 532 12.1.3 Definitions of some cosmological parameters 534 12.1.4 The redshift and its relation with the physical distance 536 12.1.5 Some important solutions to the standard ACDM model 538 12.1.6 The age of the Universe 540 12.2 Hot Big Bang and Radiation in the Early Universe 542 12.3 Neutrino Decoupling and Cosmic Neutrino Background 548 12.4 Big Bang Nucleosynthesis and Abundances of Primordial Light Elements 551 12.5 Cosmological Baryon-Antibaryon Asymmetry 555 12.6 Dark Matter 558 12.7 Dark Energy 561 12.8 Cosmic Microwave Background 565 12.8.1 Transition of the Universe to its matter-dominated epoch 565 12.8.2 Formation of the CMB 567 12.8.3 Anisotropies of the CMB 568 12.9 Three Cosmic Problems and the Inflation Mechanism 572 12.9.1 Three problems in cosmology 572 12.9.2 The inflation mechanism 574 References 578 Chapter 13. Epilogue 581 Appendix I. Calculation of Some Cross Sections 585 Appendix II. Table of Physical Constants 609 Index 617
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