1 Particles and Interactions:An Overview 1
1.1 A Preview 1
1.2 Particles 3
1.2.1 Leptons 4
1.2.2 Quarks 5
1.2.3 Hadrons 6
1.3 Interactions 6
1.4 Symmetries 10
1.5 Physical Units 13
Problems 15
Suggestions for Further Reading 16
2 Boson Fields 17
2.1 Lorentz Symmetry 18
2.1.1 Lorentz Transformations 18
2.1.2 Tensor Algebra 23
2.1.3 Tensor Fields 24
2.2 Scalar Fields 25
2.2.1 Space-Time Translation of a Scalar Field 25
2.2.2 Lorentz Transformation of a Scalar Field 28
2.3 Vector Fields 30
2.4 The Klein-Gordon Equation 31
2.4.1 Free-Particle Solutions 31
2.4.2 Particle Probability 32
2.4.3 Second Quantization 34
2.4.4 Operator Algebra 35
2.4.5 Physical Significance of the Fock Operators 37
2.5 Quantized Vector Fields 39
2.5.1 Massive Vector Fields 39
2.5.2 The Maxwell Equations 40
2.5.3 Quantization of the Electromagnetic Field 42
2.5.4 Field Energy and Momentum 46
2.6 The Action 47
2.6.1 The Euler-Lagrange Equation 47
2.6.2 Conserved Current 50
Problems 55
Suggestions for Further Reading 56
3 Fermion Fields 57
3.1 The Dirac Equation 57
3.2 Lorentz Symmetry 60
3.2.1 Covariance of the Dirac Equation 60
3.2.2 Spin of the Dirac Field 63
3.2.3 Bilinear Covariants 64
3.3 Free-Particle Solutions 65
3.3.1 Normalized Spinors 66
3.3.2 Completeness Relations 68
3.3.3 Helicities 71
3.4 The Lagrangian for a Free Dirac Particle 73
3.5 Quantization of the Dirac Field 76
3.5.1 Spins and Statistics 77
3.5.2 Dirac Field Observables 79
3.5.3 Fock Space 80
3.6 Zero-Mass Fermions 82
Problems 86
Suggestions for Further Reading 88
4 Collisions and Decays 89
4.1 Interaction Representation 90
4.1.1 The Three Pictures 90
4.1.2 Time Evolution in the Interaction Picture 92
4.1.3 The S-matrix 95
4.2 Cross-Sections and Decay Rates 96
4.2.1 General Formulas 96
4.2.2 Two-Body Reaction to Two-Body Final States 99
4.2.3 Decay Rates 103
4.3 Interaction Models 104
4.4 Decay Modes of Scalar Particles 105
4.4.1 Neutral Decay Mode 105
4.4.2 Charged Decay Mode 108
4.5 Pion Scattering 109
4.5.1 The Scalar Boson Propagator 110
4.5.2 Scattering Processes 112
4.5.3 Summary and Generalization 116
4.6 Electron-Proton Scattering 118
4.6.1 The Electromagnetic Interaction 119
4.6.2 Electron-Proton Scattering Cross-Section 120
4.7 Electron-Positron Annihilation 127
4.8 Compton Scattering 133
Problems 141
Suggestions for Further Reading 142
5 Discrete Symmetries 143
5.1 Parity 144
5.1.1 Parity in Quantum Mechanics 144
5.1.2 Parity in Field Theories 146
5.1.3 Parity and Interactions 150
5.2 Time Inversion 155
5.2.1 Time Inversion in Quantum Mechanics 156
5.2.2 Time Inversion in Field Theories 158
5.2.3 T and Interactions 162
5.3 Charge Conjugation 163
5.3.1 Additive Quantum Numbers 164
5.3.2 Charge Conjugation in Field Theories 169
5.3.3 Interactions 174
5.4 The CPT Theorem 178
5.4.1 Implications of CPT Invariance 180
5.4.2 C,P,T,and CPT 181
Problems 182
Suggestions for Further Reading 184
6 Hadrons and Isospin 185
6.1 Charge Symmetry and Charge Independence 185
6.2 Nucleon Field in Isospin Space 187
6.3 Pion Field in Isospin Space 193
6.4 G-Parity 198
6.4.1 Nucleon and Pion Fields 199
6.4.2 Other Unflavored Hadrons 204
6.5 Isospin of Strange Particles 205
6.6 Isospin Violations 207
6.6.1 Electromagnetic Interactions 207
6.6.2 Weak Interactions 208
Problems 213
Suggestions for Further Reading 214
7 Quarks and SU(3)Symmetry 215
7.1 Isospin:SU(2)Symmetry 216
7.2 Hypercharge:SU(3)Symmetry 222
7.2.1 The Fundamental Representation 222
7.2.2 Higher-Dimensional Representations 224
7.2.3 Physical Significance of F3 and F8 228
7.2.4 3×3＊ Equal Mesons 230
7.2.5 3×3×3 Equal Baryons 233
7.3 Mass Splitting of the Hadron Multiplets 236
7.3.1 Baryons 238
7.3.2 Mesons 239
7.4 Including Spin:SU(6) 241
7.4.1 Mesons 243
7.4.2 Baryons 245
7.4.3 Application:Magnetic Moments of Hadrons 246
7.5 The Color of Quarks 248
7.6 The New Particles 250
7.6.1 J/ψ and Charm 250
7.6.2 The Tau Lepton 258
7.6.3 From Bottom to Top 260
Problems 263
Suggestions for Further Reading 265
8 Gauge Field Theories 267
8.1 Symmetries and Interactions 267
8.2 Abelian Gauge Invariance 269
8.3 Non-Abelian Gauge Invariance 271
8.4 Quantum Chromodynamics 277
8.5 Spontaneous Breaking of Global Symmetries 283
8.5.1 The Basic Idea 284
8.5.2 Breakdown of Discrete Symmetry 286
8.5.3 Breakdown of Abelian Symmetry 287
8.5.4 Breakdown of Non-Abelian Symmetry 289
8.6 Spontaneous Breaking of Local Symmetries 293
8.6.1 Abelian Symmetry 293
8.6.2 Non-Abelian Symmetry 298
Problems 301
Suggestions for Further Reading 303
9 The Standard Model of the Electroweak Interaction 305
9.1 The Weak Interaction Before the Gauge Theories 305
9.2 Gauge-Invariant Model of One-Lepton Family 307
9.2.1 Global Symmetry 308
9.2.2 Gauge Invariance 312
9.2.3 Spontaneous Symmetry Breaking 313
9.2.4 Feynman Rules for One-Lepton Family 322
9.3 Including u and d Quarks 326
9.4 Multigeneration Model 330
9.4.1 The GIM Mechanism 330
9.4.2 Classification Scheme for Fermions 333
9.4.3 Fermion Families and the CKM Matrix 333
9.4.4 Summary and Extensions 338
Problems 341
Suggestions for Further Reading 342
10 Electron-Nucleon Scattering 343
10.1 Electromagnetic and Weak Form Factors 343
10.2 Analyticity and Dispersion Relation 352
10.3 Exclusive Reaction:Elastic Scattering 355
10.4 Inclusive Reaction:Deep Inelastic Scattering 361
10.4.1 Structure Functions 362
10.4.2 Bjorken Scaling and the Feynman Quark Parton 366
Problems 373
Suggestions for Further Reading 375
11 Neutral K Mesons and CP Violation 377
11.1 The Two Neutral K Mesons 378
11.2 Strangeness Oscillations 380
11.3 Regeneration of Ko s 383
11.4 Calculation of △m 385
11.5 CP Violation 389
11.5.1 General Formalism 389
11.5.2 Model-Independent Analysis of KL→2π 393
11.5.3 The Superweak Scenario 398
11.5.4 Calculations of ε and ε′ in the Standard Model 399
11.5.5 The Gluonic Penguin and |ε′/ε| 402
Problems 406
Suggestions for Further Reading 406
12 The Neutrinos 407
12.1 On the Neutrino Masses 407
12.1.1 General Properties 408
12.1.2 Dirac or Majorana Neutrino? 409
12.1.3 Lepton Mixing 411
12.2 Oscillations in the Vacuum 412
12.3 Oscillations in Matter 415
12.3.1 Index of Refraction,Effective Mass 416
12.3.2 The MSW Effect 420
12.3.3 Adiabaticity 423
12.4 Neutral Currents by Neutrino Scattering 426
12.4.1 Neutral Currents,Why Not? 427
12.4.2 Neutrino-Electron Scattering 428
12.5 Neutrino-Nucleon Elastic Scattering 435
12.6 Neutrino-Nucleon Deep Inelastic Collision 438
12.6.1 Deep Inelastic Cross-Section 439
12.6.2 Quarks as Partons 441
Problems 445
Suggestions for Further Reading 446
13 Muon and Tau Lepton Decays 447
13.1 Weak Decays:Classification and Generalities 447
13.2 Leptonic Modes 450
13.2.1 Leptonic Branching Ratio 450
13.2.2 Parity Violation.Energy Spectrum 451
13.2.3 Angular Distribution.Decay Rate 456
13.3 Semileptonic Decays 460
13.3.1 The Ohe-Pion Mode：τ-→ντ＋π- 460
13.3.2 The 2n-Pion Mode and CVC 462
13.4 The Method of Spectral Functions 465
13.4.1 The Three-Pion Mode 467
13.4.2 Spectral Functions of Quark Pairs 470
Problems 473
Suggestions for Further Reading 474
14 One-Loop QCD Corrections 475
14.1 Vertex Function 477
14.2 Quark Self-Energy 484
14.3 Mass and Field Renormalization 485
14.3.1 Renormalized Form Factor ？ren(q2) 489
14.3.2 Important Consequence of Mass Renormalization 491
14.4 Virtual Gluon Contributions 492
14.5 Real Gluon Contributions 496
14.5.1 Infrared Divergence 497
14.5.2 Three-Particle Phase Space 498
14.5.3 Bremsstrahlung Rate 500
14.6 Final Result 501
Problems 502
Suggestions for Further Reading 504
15 Asymptotic Freedom in QCD 505
15.1 Running Coupling Constant 506
15.1.1 Vacuum Polarization 507
15.1.2 Dressed and Renormalized Photon Propagator 509
15.1.3 Vertex Renormalization 512
15.1.4 Renormalized Vacuum Polarization ？ren(q2) 515
15.1.5 Physical Effects of ？ren(q2) 517
15.2 The Renormalization Group 518
15.2.1 The Callan-Symanzik Equation 520
15.2.2 Calculation of the β- and γ-Functions 523
15.2.3 Running Coupling from the Renormalization Group 525
15.2.4 Solution of the Renormalization Group Equation 526
15.3 One-Loop Computation of the QCD β-Function 529
15.3.1 Quark Self-Energy Counterterm Zq 529
15.3.2 Quark-Gluon Vertex Counterterm Zl 529
15.3.3 Gluon Self-Energy Counterterm Zglu 531
15.3.4 The Running QCD Coupling 535
15.4 Ghosts 538
15.4.1 The Faddeev-Popov Gauge-Fixing Method 538
15.4.2 Ghosts and Unitarity 541
Problems 547
Suggestions for Further Reading 548
16 Heavy Flavors 549
16.1 QCD Renormalization of Weak Interactions 550
16.1.1 Corrections to Single Currents 551
16.1.2 Corrections to Product of Currents 553
16.1.3 Renormalization Group Improvement 557
16.1.4 The △I=1/2 in Strangeness Hadronic Decays 560
16.2 Heavy Flavor Symmetry 562
16.2.1 Basic Physical Pictures 563
16.2.2 Elements of Heavy Quark Effective Theory(HQET) 565
16.3 Inclusive Decays 567
16.3.1 General Formalism 568
16.3.2 Inclusive Semileptonic Decay:？→e-+？e+Xc 572
16.3.3 Inclusive Nonleptonic Decay:？→Hadrons 573
16.4 Exclusive Decays 576
16.4.1 Form Factors in B？3 Decays 577
16.4.2 Semileptonic Decay Rates 580
16.4.3 Two-Body Hsdronic Decays 582
16.5 CP Violationin B Mesons 588
16.5.1 B0-？0 Mixing 588
16.5.2 CP Asymmetries in Neutral B Meson Decays 594
Problems 598
Suggestions for Further Reading 599
17 Status and Perspectives of the Standard Model 601
17.1 Production and Decay of the Higgs Boson 602
17.2 Why Go Beyond the Standard Model? 605
17.3 The Standard Model as an Effective Theory 607
17.3.1 Problems with the Standard Model 608
17.3.2 Renormalization Group Equation Analysis 610
17.3.3 Supersymmetry and Technicolor 611
Problems 614
Suggestions for Further Reading 614
Selected Solutions 615
Appendix:Useful Formulas 645
A.1 Relativistic Quantum Mechanics 645
A.2 Cross-Sections and Decay Rates 649
A.3 Phase Space and Loop Integrals 650
A.4 Feynman Rules 653
A.5 Parameters of the Standard Model 656
Index 657