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Tables of Contents for An Introduction to Quantum Field Theory
Chapter/Section Title
Page #
Page Count
Preface
xi
Notations and Conventions
xix
Editor's Foreword
xxii
Part I: Feynman Diagrams and Quantum Electrodynamics
Invitation: Pair Production in e+e- Annihilation
3
10
The Klein-Gordon Field
13
22
The Necessity of the Field Viewpoint
13
2
Elements of Classical Field Theory
15
4
The Klein-Gordon Field as Harmonic Oscillators
19
6
The Klein-Gordon Field in Space-Time
25
10
Problems
33
2
The Dirac Field
35
42
Lorentz Invariance in Wave Equations
35
5
The Dirace Equation
40
5
Free-Particle Solutions of the Dirac Equation
45
4
Dirac Matrices and Dirac Field Bilinears
49
3
Quantization of the Dirac Field
52
12
Discrete Symmetries of the Dirac Theory
64
13
Problems
71
6
Interacting Fields and Feynman Diagrams
77
54
Perturbation Theory---Philosophy and Examples
77
5
Perturbation Expansion of Correlation Functions
82
6
Wick's Theorem
88
2
Feynman Diagrams
90
9
Cross Sections and the S-Matrix
99
9
Computing S-Matrix Elements from Feynman Diagrams
108
7
Feynman Rules for Fermions
115
8
Feynman Rules for Quantum Electrodynamics
123
8
Problems
126
5
Elementary Processes of Quantum Electrodynamics
131
44
e+e-→ μ+μ-: Introduction
131
10
e+e- → μ+μ-: Helicity Structure
141
5
e+e- → μ+μ-: Nonrelativistic Limit
146
7
Crossing Symmetry
153
5
Compton Scattering
158
17
Problems
169
6
Radiative Corections: Introduction
175
36
Soft Bremsstrahlung
176
8
The Electron Vertex Function: Formal Structure
184
5
The Electron Vertex Function: Evaluation
189
10
The Electron Vertex Function: Infrared Divergence
199
3
Summation and Interpretation of Infrared Divergences
202
9
Problems
208
3
Radiative Corrections: Some Formal Developments
211
54
Field-Strength Renormalization
211
11
The LSZ Reduction Formula
222
8
The Optical Theorem
230
8
The Ward-Takahashi Identity
238
6
Renormalization of the Electric Charge
244
21
Problems
257
2
Final Project: Radiation of Gluon Jets
259
6
Part II: Renormalization
Invitation: Ultraviolet Cutoffs and Critical Fluctuations
265
10
Functional Methods
275
40
Path Integrals in Quantum Mechanics
275
7
Functional Quantization of Scalar Fields
282
10
Quantum Field Theory and Statistical Mechanics
292
2
Quantization of the Electromagnetic Field
294
4
Functional Quantization of Spinor Fields
298
8
Symmetries in the Functional Formalism
306
9
Problems
312
3
Systematics of Renormalization
315
32
Counting of Ultraviolet Divergences
315
8
Renormalized Perturbation Theory
323
7
Renormalization of Quantum Electrodynamics
330
5
Renormalization Beyond the Leading Order
335
3
A Two-Loop Example
338
9
Problems
344
3
Renormalization and Symmetry
347
46
Spontaneous Symmetry Breaking
348
4
Renormalization and Symmetry: An Explicit Example
352
12
The Effective Action
364
6
Computation of the Effective Action
370
9
The Effective Action as a Generating Functional
379
4
Renormalization and Symmetry: General Analysis
383
10
Problems
389
4
The Renormalization Group
393
46
Wilson's Approach to Renormalization Theory
394
12
The Callan-Symanzik Equation
406
12
Evolution of Coupling Constants
418
10
Renormalization of Local Operators
428
4
Evolution of Mass Parameters
432
7
Problems
438
1
Critical Exponents and Scalar Field Theory
439
34
Theory of Critical Exponents
440
11
Critical Behavior in Four Dimensions
451
3
The Nonlinear Sigma Model
454
19
Problems
466
3
Final Project: The Coleman-Weinberg Potential
469
4
Part III: Non-Abelian Gauge Theories
Invitation: The Parton Model of Hadron Structure
473
8
Non-Abelian Gauge Invariance
481
24
The Geometry of Gauge Invariance
482
4
The Yang-Mills Lagrangian
486
5
The Gauge-Invariant Wilson Loop
491
4
Basic Facts About Lie Algebras
495
10
Problems
502
3
Quantization of Non-Abelian Gauge Theories
505
40
Interactions of Non-Abelian Gauge Bosons
506
6
The Faddeev-Popov Lagrangian
512
3
Ghosts and Unitarity
515
2
BRST Symmetry
517
4
One-Loop Divergences of Non-Abelian Gauge Theory
521
12
Asymptotic Freedom: The Background Field Method
533
8
Asymptotic Freedom: A Qualitative Explanation
541
4
Problems
544
1
Quantum Chromodynamics
545
54
From Quarks to QCD
545
3
e+e- Annihilation into Hadrons
548
7
Deep Inelastic Scattering
555
8
Hard-Scattering Processes in Hadron Collisions
563
11
Parton Evolution
574
19
Measurements of αs
593
6
Problems
595
4
Operator Products and Effective Vertices
599
52
Renormalization of the Quark Mass Parameter
599
6
QCD Renormalization of the Weak Interactions
605
7
The Operator Product Expansion
612
3
Operator Analysis of e+e- Annihilation
615
6
Operator Analysis of Deep Inelastic Scattering
621
30
Problems
647
4
Perturbation Theory Anomalies
651
38
The Axial Current in Two Dimensions
651
8
The Axial Current in Four Dimensions
659
8
Goldstone Bosons and Chiral Symmetries in QCD
667
9
Chiral Anomalies and Chiral Gauge Theories
676
6
Anomalous Breaking of Scale Invariance
682
7
Problems
686
3
Gauge Theories with Spontaneous Symmetry Breaking
689
42
The Higgs Mechanism
690
10
The Glashow-Weinberg-Salam Theory of Weak Interactions
700
19
Symmetries of the Theory of Quarks and Leptons
719
12
Problems
728
3
Quantization of Spontaneously Broken Gauge Theories
731
50
The Rξ Gauges
732
11
The Goldstone Boson Equivalence Theorem
743
15
One-Loop Corrections in Weak-Interaction Gauge Theory
758
23
Problems
773
2
Final Project: Decays of the Higgs Boson
775
6
Epilogue
Quantum Field Theory at the Frontier
781
20
Strong Strong Interactions
782
4
Grand Unification and its Paradoxes
786
5
Exact Solutions in Quantum Field Theory
791
4
Supersymmetry
795
3
Toward an Ultimate Theory of Nature
798
3
Appendix: Reference Formulae
801
10
A.1 Feynman Rules
801
2
A.2 Polarizations of External Particles
803
2
A.3 Numerator Algebra
805
1
A.4 Loop Integrals and Dimensional Regularization
806
2
A.5 Cross Sections and Decay Rates
808
1
A.6 Physical Constants and Conversion Factors
809
2
Bibliography
811
6
Index
817