Particle Physics and Introduction to Field Theory

876 Pages·1981·29.48 MB·English

by  T.D. Lee

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Particle
Physics
ana
Introduction
to Field
Theory
Contemporary
A series edited by
Henry Primakoff,
Concepts
University of Pennsylvania
in Physics Associate Editors:
Eli Burstein
University of Pennsylvania
Willis Lamb
University of Arizona
Leon Lederman
Fermi National
Accelerator Laboratory
Sir Rudolf Peierls
Oxford University
Mal Ruderman
Columbia University
Volume 1
Particle Physics
and Introduction
to Field Theory
Additional volumes
in preparation.
Science Press (Beijing)
Particle
Physics
ana
Introduction
to Field
Theory
T.D. Lee
Columbia University
CRC Press
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TO JEANNETTE
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Contents
Preface to the Series . . • . . . . . . . . . . . . . . • . . . . • . . . xv
Preface xvii
Part I: Introduction to Field Theory
Chapter 1: Mechanics of a Finite System {Review) • • • • • • 3
1.1 Classical Mechanics • • • • • • • • • • • • • • • • • • • 3
1. 2 Quantization . . . . . . . . . . . . . . . . . . . . . . • . 4
1.3 Some Genera I Theorems • • • • • • • • • • • • • . • • 10
Chapter 2: The Spin-O Field • • • • • • • • • • • • • • • • .. • • 17
2.1 General Discussion • • • • • • • • . . • • • • . • • • • 17
2.2 Fourier Expansion (Free or Interacting Fields) • • • 20
2.3 Hilbert Space (Free or Interacting Fields) • . • • • 25
Chapter 3 : The Spin-! Field • • • • • • • • • • • • • • • • • • • • 29
3.1 Mathematical Preliminaries • • • . • • • • • • • • • • 29
3.2 Free Field . • • . . . . . . . . . . • • • • • • . • . • . . 31
3.3 Quantization (Free or Interacting Fields) • • • • • 32
3.4 Fourier Expansion {Free or Interacting Fields) • • • 34
3.5 Hilbert Space (Free or Interacting Fields) • • • • • 37
3.6 Momentum and Angular Momentum Operators • • • 41
3.7 Phase Factor Conventions between the Spinors • • 45
3.8 Two-component Theory • . • . • • • • • • • • • • • • • 49
Chapter 4: The Spin-1 Field (m I 0) •••••••.••••• 55
4. 1 Free Field ..........•.......•....•• 55
4.2 I11h~rading Field$ 58
Chapter 5: Feynman Diagrams 62
5.1 Heisenberg, Schr!XIinger
and Interaction Representations • 62
5.2 S-Matrix 66
vii.
5.3 Time-ordered Products, Normal Products
and Contractions 72
5.4 Perturbation Series •.•••••••.•.•...••• 78
5. 5 Wick Theorem ••••••••••.••.•.••.••• 80
5.6 App I i cations • . • • • • • . . • . • . . . • • • • • • . • 84
5.7 Differential Cross Sections for 1 + 2 - 1' + 2'
+ ..• + n' 92
Chapter 6 : Quantum Electrodynamics 103
6.1 Lagrangian •••..•••..•••.••••.••••• 103
6.2 Coulomb Gauge ••.•••••....•..•..•• 104
6.3 Quantization •••••.•••.••..••••••.• 107
6.4 Photon Propagator and Relativistic Invariance 109
6.5 Remarks •..•.••••••••••••••..•.••• 113
Chapter 7: Solitons 117
7.1 Early History . . • • • . • . . • • . • . . . . • • • . • 117
7.2 Definition, Classification and Some General Remarks 123
7.3 One-space-dimensional Examples • . • . . • • • • 128
-Topological soliton. Nontopological soliton.
7.4 Derrick Theorem . • • • . • • • • • • • • . • • • . . . 138
7.5 Solitons vs. Plane Waves . • • • . • • . • • . • • • 141
-One space-dimension. Two space-dimensions.
Three space-dimensions.
7.6 Quantization • • . • . • • • • • • • • • . • • • . . . • 150
-Lagrangian, Hamiltonian and commutation relations.
Coli ecti ve coordinates. Perturbation expansion.
Part II : Particle Physics
Chapter 8 : Order-of-magnitude Estimations 161
8.1 Radius of the Hydrogen Atom • • • • . . • • • . • 162
8.2 Hadron Size • • . • . . • . . . • • • • • • • . . . • • . 163
8.3 High-energy pp, 1rp and Kp Total Cross Sections 164
8.4 e+ + e- - (J+ + fJ- • • • • • • • • • • • . • • • • • • 165
8.5 v + N - ••· • • • • • • • • • . . • . • • • • . . . • 167
8.6 Compton Scattering • . • • • • . . . . . . • . • . . . 168
8.7 Mass Singularity and High-energy Behavior 170
8.8 e+ e- Pair Production by High-energy Photons 173
viii.
Part IIA: Particle Physics: Symmetry
Chapter 9 : General Discussion 177
9.1 Non-observables, Symmetry Transformations
and Conservation Laws 178
9.2 Asymmetries and Observables • • • . • • • • • • . • 181
u
Chapter 10 : 1 Symmetry and P, C Invari once • • • • • 189
10.1 QED as an Example • . . • . . • . • . • • . • • • • 189
10.2 Applications . • • • . . . . • . • . • • . . • • • • • . 199
-Furry theorem. Positronium states. Decay of a
f
spin-0 particle - 2y. Spin-1 particle 2y.
10.3 General Discussion • • • • . • • • • • • • • • • • . • 208
10.4 Baryon Number and Lepton Number • • . • • • • 210
Chapter 11 Isotopic Spin and G Parity 217
11. 1 lsospi n • • • . • . . • • • • • • • • • • . • • • • • . • • 21 7
-u
2 symmetry. lsospi n transformations.
11.2 G Parity • . . • • • . • • . • . • . • • . • • . . . . • 225
-Nucleon-antinucleon system. The quantum num
ber G.
11.3 Applications to Mesons and Baryons • . • . . • • 230
-Pion. Vector mesons. A and kaon. Meson and
baryon octets.
11.4 Isospin Violation • • • • . • • • • • • • • • . • • • • • 240
-Electromagnetic interaction. Weak interaction.
u
Chapter 12 : S 3 Symmetry • • • • • • • . • • • • • • • • • • • 251
12.1 Mathematical Preliminary . • • . • • • • • • • • • 253
-Tensors. Representations. Decomposition of
® ® .
x Some further properties. Excur-
sion to other groups.
12.2 Hadron States and Their Flavor and Color
Symmetries • 265
-Pseudoscalar octet. Baryon spin--! octet and
spin·~ decuplet.
12.3 Mass Formulas • • • • • • • • • • • • • . • • • • • . • 273
-Hasym and the spurion formulation. Octet mass
formulas. Decuplet mass formula.
ix.