Table of Contents
Preface (for the 21st-century Edition) v
Preface (for the 1st Edition) vii
Foreword ix
Chapter 0 We Live in the Quantum 4-Dimensional Minkowski Space-Time 1
0.0 The Space-Time
0.1 The Point in the Quantum Sense
0.2 The Standard Model of the 20th Century
0.3 From Building Blocks of Matter to the Smallest Units of Matter
0.4 The Standard Model of All Centuries
0.5 The Origin of Mass
0.6 The Origin of Fields (Point-Like Particles)
0.7 A Few Words about Gravity
Part. A Relativistic Quantum Mechanics
Chapter 1 The Language 16
1 The Axioms Leading to Quantum Fields
2 Our Universe
3 The Concepts Developed in the 20th Century
4 Renormalizability
5 Relativistic Quantum Mechanics
6 The Declaration
Appendix: Introduction on the Curved Space-Time
Chapter 2 The Dime Theory for Free Electrons 41
2.1 Dirac's Relativistic Equation
2.2 Solution of Dirac's Equation for a Free Electron
2.3 The Early Puzzles in Terms of Negative-Energy States
2.4 Electron Spin
2.5 Foldy-Wouthuysen Representation
Chapter 3 γμ-Matrices; Helicity; Charge Conjugation 69
3.1 Properties of the γμ Matrices
3.2 Helicity and Neutrinos
3.3 Charge Conjugation
3.4 Dirac Equation in Majorana. Representation
Chapter 4 Transformations of the Dirac Equation 89
4.1 Unitary Transformations
4.2 Gauge Transformations
4.3 Lorentz Transformations
4.4 Space Inversion, Charge Conjugation, and Time Reversal
4.5 The Transformation Matrix S
Chapter 5 The Dirac Electron in an Electromagnetic Field 107
5.1 Dirac Equations in Second-Order Form
5.2 Dirac Equation: Approximate. Iterated Form
5.3 Hydrogcirie Atoms in Dirac's Theory - Approximate Solution
5.4 Hydrogenic Atoms in Dirac's Theory - Exact. Solution
5.5 Dirac Equation and Many-Body Features
5.6 "Extra Moments" to the Dirac Equation?
Part B Introduction to Quantum Field Theory
Chapter 6 Classical Fields 131
6.1 Introduction
6.2 Classical Field Equation
6.3 Noether's Theorem
6.4 The Klein-Gordon Field in Lagrangian Form
6.5 The Electromagnetic Field in Lagrangian Form
6.6 The Dirac Field in Lagrangian Form
Appendix: Electromagnetic Fields
Chapter 7 Many-Body Systems 158
7.1 Permutations
7.2 Symmetric and Antisymmetric Wave Functions for Fermions and Bosons
7.3 Fock Representation: Creation and Annihilation Operators
7.4 Neutrino Halos in Our Universe
7.5 Black Holes do not Exist in Our Universe
Chapter 8 Quantization of Free Fields 178
8.1 Klein-Gordon, Real (Pseudo) Scalar Field φ(xμ)
8.2 Klein-Gordon Complex, Scalar Field
8.3 Electromagnetic Fields
8.4 Dirac Electron-Positron Field
8.5 Dirac's Theory of Emission and Absorption of Radiation
Appendix: Green's Functions Δ and D
Chapter 9 Quantum Electrodynamics I: S-Matrix Elements 212
9.1 The Evolution Operator and the S-Matrix
9.2 S-Matrix Elements and Feynman Rules
9.3 Calculation of Cross Sections;
Chapter 10 Quantum Electrodynamics II: Renormalization 232
10.1 Pauli-Villars Regularization
10.2 Dimensional Regularization
10.3 Introduction to Renormalization
Appendix: Some Useful Formulae for Dimensional Regularization
Part C The Standard Model
Chapter 11 Symmetries, Transformations, and Invariants 257
11.1 SU(2) Symmetries in Particle Physics
11.2 Flavor SU(3) Symmetry: Isospin and Strangeness
11.3 Additional Symmetries in Particle Physics
Appeudix; Potentials and Phase in Quantum Mechanics
Chapter 12 Quantum Chromodynamics 293
12.1 QCD is an SU(3) Gauge Theory
12.2 QCD is Asymptotically Free
12.3 Color Confinement
Appendix A Method of Path Integrals
Appendix B Method of Lattice Gauge Fields
Chapter 13 The Glashow-Salam-Weinberg Electroweak Theory 316
13.1 Higgs Mechanism in an SU(2) × U(⊥) Gauge Theory
13.2 The SU(2) × U(1) Electroweak Theory with Two Generations of Fermions
13.3 Weak Interactions at Low Energies
Appendix: Feynman Rules in the Rξ Gauge
Chapter 14 Experimental Tests: The Standard Model of the 20th Century 337
14.1 Quantum Chromodynamics
14.2 The Glashow-Salam-Weinberg SU(2) × U(1) Electroweak Theory
14.3 Concluding Remarks
Chapter 15 The Standard Model 359
15.1 Prelude
15.2 The Origin of Mass
15.3 Leptons: Point-Like Dirac Particles
15.4 The Standard Model of All Centuries
15.5 Conehiding Remarks
15.6 The Episode
Chapter 16 Neutrinos in the Cosmos 379
16.1 Prelude
16.2 The Standard Model of All Centuries
16.3 v(Solar) + ν(CB; kνF) → e- + e+ as the Evidence
16.4 Invisible Neutrino Halos and Black Holes
16.5 Concluding Remarks
Subject Index 391
Name Index 399
