Quantum Field Theory A Modern Introduction
Half-Title
Title Page
Copyright
Dedication
Preface
Acknowledgments
Contents
Part I: Quantum Fields and Renormalization
1. Why Quantum Field Theory?
1.1 Historical Perspective
1.2 Strong Interactions
1.3 Weak Interactions
1.4 Gravitational Interaction
1.5 Gauge Revolution
1.6 Unification
1.7 Action Principle
1.8 From First to Second Quantization
1.9 Noether's Theorem
1.10 Exercises
2. Symmetries and Group Theory
2.1 Elements of Group Theory
2.2 SO(2)
2.3 Representations of SO(2) and U(1)
2.4 Representations of SO(3) and SU(2)
2.5 Representations of SO(N)
2.6 Spinors
2.7 Lorentz Group
2.8 Representations of the PoincarΓ© Group
2.9 Master Groups and Supersymmetry
2.10 Exercises
3. Spin-0 and Β½ Fields
3.1 Quantization Schemes
3.2 Klein-Gordon Scalar Field
3.3 Charged Scalar Field
3.4 Propagator Theory
3.5 Dirac Spinor Field
3.6 Quantizing the Spinor Field
3.7 Weyl Neutrinos
3.8 Exercises
4. Quantum Electrodynamics
4.1 Maxwell's Equations
4.2 Relativistic Quantum Mechanics
4.3 Quantizing the Maxwell Field
4.4 Gupta-Bleuler Quantization
4.5 C, P, and T Invariance
4.5.1 Parity
4.5.2 Charge Conjugation
4.5.3 Time Reversal
4.6 CPT Theorem
4.7 Exercises
5. Feynman Rules and LSZ Reduction
5.1 Cross Sections
5.2 Propagator Theory and Rutherford Scattering
5.3 LSZ Reduction Formulas
5.4 Reduction of Dirac Spinors
5.5 Time Evolution Operator
5.6 Wick's Theorem
5.7 Feynman's Rules
5.8 Exercises
6. Scattering Processes and the S Matrix
6.1 Compton Effect
6.2 Pair Annihilation
6.3 MΓΈller Scattering
6.4 Bhabha Scattering
6.5 Bremsstrahlung
6.6 Radiative Corrections
6.7 Anomalous Magnetic Moment
6.8 Infrared Divergence
6.9 Lamb Shift
6.10 Dispersion Relations
6.11 Exercises
7. Renormalization of QED
7.1 The Renormalization Program
7.2 Renormalization Types
7.2.1 Nonrenormalizable Theories
7.2.2 Renormalizable Theories
7.2.3 Super-renormalizable Theories
7.2.4 Finite Theories
7.3 Overview of Renormalization in Οβ΄ Theory
7.4 Overview of Renormalization in QED
7.5 Types of Regularization
7.6 Ward-Takahashi Identities
7.7 Overlapping Divergences
7.8 Renormalization of QED
7.8.1 Step One
7.8.2 Step Two
7.8.3 Step Three
7.8.4 Step Four
7.9 Exercises
Part II: Gauge Theory and the Standard Model
8. Path Integrals
8.1 Postulates of Quantum Mechanics
8.1.1 Postulate I
8.1.2 Postulate II
8.2 Derivation of the SchrΓΆdinger Equation
8.3 From First to Second Quantization
8.4 Generator of Connected Graphs
8.5 Loop Expansion
8.6 Integration over Grassmann Variables
8.7 Schwinger-Dyson Equations
8.8 Exercises
9. Gauge Theory
9.1 Local Symmetry
9.2 Faddeev-Popov Gauge Fixing
9.3 Feynman Rules for Gauge Theory
9.4 Coulomb Gauge
9.5 The Gribov Ambiguity
9.6 Equivalence of the Coulomb and Landau Gauge
9.7 Exercises
10. The Weinberg-Salam Model
10.1 Broken Symmetry in Nature
10.2 The Higgs Mechanism
10.3 Weak Interactions
10.4 Weinberg-Salam Model
10.5 Lepton Decay
10.6 R_ΞΎ Gauge
10.7 't Hooft Gauge
10.8 Coleman-Weinberg Mechanism
10.9 Exercises
11. The Standard Model
11.1 The Quark Model
11.2 QCD
11.2.1 Spin-Statistics Problem
11.2.2 Pair Annihilation
11.2.3 Jets
11.2.4 Absence of Exotics
11.2.5 Pion Decay
11.2.6 Asymptotic Freedom
11.2.7 Confinement
11.2.8 Chiral Symmetry
11.2.9 No Anomalies
11.3 Jets
11.4 Current Algebra
11.5 PCAC and the Adler-Weisberger Relation
11.5.1 CVC
11.5.2 PCAC
11.5.3 Adler-Weisberger Relation
11.6 Mixing Angle and Decay Processes
11.6.1 Purely Leptonic Decays
11.6.2 Semileptonic Decays
11.6.3 Nonleptonic Decays
11.7 GIM Mechanism and Kobayashi-Maskawa Matrix
11.8 Exercises
12. Ward Identities, BRST, and Anomalies
12.1 Ward-Takahashi Identity
12.2 Slavnov-Taylor Identities
12.3 BRST Quantization
12.4 Anomalies
12.5 Non-Abelian Anomalies
12.6 QCD and Pion Decay into Gamma Rays
12.7 Fujikawa's Method
12.8 Exercises
13. BPHZ Renormalization of Gauge Theories
13.1 Counterterms in Gauge Theory
13.2 Dimensional Regularization of Gauge Theory
13.3 BPHZ Renormalization
13.4 Forests and Skeletons
13.5 Does Quantum Field Theory Really Exist?
13.6 Exercises
14. QCD and the Renormalization Group
14.1 Deep Inelastic Scattering
14.2 Parton Model
14.3 Neutrino Sum Rules
14.4 Product Expansion at the Light-Cone
14.5 Renormalization Group
14.6 Asymptotic Freedom
14.7 Callan-Symanzik Relation
14.8 Minimal Subtraction
14.9 Scale Violations
14.10 Renormalization Group Proof
14.10.1 Step One
14.10.2 Step Two
14.10.3 Step Three
14.11 Exercises
Part III: Nonperturbative Methods and Unification
15. Lattice Gauge Theory
15.1 The Wilson Lattice
15.2 Scalars and Fermions on the Lattice
15.3 Confinement
15.4 Strong Coupling Approximation
15.5 Monte Carlo Simulations
15.6 Hamiltonian Formulation
15.7 Renormalization Group
15.8 Exercises
16. Solitons, Monopoles, and Instantons
16.1 Solitons
16.1.1 Example: Οβ΄
16.1.2 Example: Sine-Gordon Equation
16.1.3 Example: Nonlinear O(3) Model
16.2 Monopole Solutions
16.3 't Hooft-Polyakov Monopole
16.4 WKB, Tunneling, and Instantons
16.5 Yang-Mills Instantons
16.6 ΞΈ Vacua and the Strong CP Problem
16.7 Exercises
17. Phase Transitions and Critical Phenomena
17.1 Critical Exponents
17.2 The Ising Model
17.2.1 XYZ Heisenberg Model
17.2.2 IRF and Vertex Models
17.3 Yang-Baxter Relation
17.4 Mean-Field Approximation
17.5 Scaling and the Renormalization Group
17.5.1 Step One
17.5.2 Step Two
17.5.3 Step Three
17.5.4 Step Four
17.6 Ο΅ Expansion
17.7 Exercises
18. Grand Unified Theories
18.1 Unification and Running Coupling Constants
18.2 SU(5)
18.3 Anomaly Cancellation
18.4 Fermion Representation
18.5 Spontaneous Breaking of SU(5)
18.6 Hierarchy Problem
18.7 SO(10)
18.8 Beyond GUT
18.8.1 Technicolor
18.8.2 Preons or Subquarks
18.8.3 Supersymmetry and Superstrings
18.9 Exercises
19. Quantum Gravity
19.1 Equivalence Principle
19.2 Generally Covariant Action
19.3 Vierbeins and Spinors in General Relativity
19.4 GUTs and Cosmology
19.5 Inflation
19.6 Cosmological Constant Problem
19.7 Kaluza-Klein Theory
19.8 Generalization to Yang-Mills Theory
19.9 Quantizing Gravity
19.10 Counterterms in Quantum Gravity
19.11 Exercises
20. Supersymmetry and Supergravity
20.1 Supersymmetry
20.2 Supersymmetric Actions
20.3 Superspace
20.4 Supersymmetric Feynman Rules
20.5 Nonrenormalization Theorems
20.6 Finite Field Theories
20.7 Super Groups
20.8 Supergravity
20.9 Exercises
21. Superstrings
21.1 Why Strings?
21.2 Points versus Strings
21.3 Quantizing the String
21.3.1 Gupta-Bleuler Quantization
21.3.2 Light-Cone Gauge
21.3.3 BRST Quantization
21.4 Scattering Amplitudes
21.5 Superstrings
21.6 Types of Strings
21.6.1 Type I
21.6.2 Type IIA
21.6.3 Type lIB
21.6.4 Heterotic String
21.7 Higher Loops
21.8 Phenomenology
21.9 Light-Cone String Field Theory
21.10 BRST Action
21.11 Exercises
Appendix
A.1 SU(N)
A.2 Tensor Products
A.3 SU(3)
A.4 Lorentz Group
A.S Dirac Matrices
A.6 Infrared Divergences to All Orders
A.7 Dimensional Regularization
Notes
Chapter 1. Why Quantum Field Theory?
Chapter 3. Spin 0 and Β½ Fields
Chapter 4. Quantum Electrodynamics
Chapter 5. Feynman Rules and Reduction
Chapter 6. Scattering Processes and the S-Matrix
Chapter 7. Renormalization of QED
Chapter 8. Path Integrals
Chapter 9. Gauge Theory
Chapter 10. The Weinberg-Salam Model
Chapter 11. The Standard Model
Chapter 12. Ward Identities, BRST, and Anomalies
Chapter 13. BPHZ Renormalization of Gauge Theories
Chapter 14. QCD and the Renormalization Group
Chapter 15. Lattice Gauge Theory
Chapter 16. Solitons, Monopoles, and Instantons
Chapter 17. Phase Transitions and Critical Phenomena
Chapter 18. Grand Unified Theories
Chapter 19. Quantum Gravity
Chapter 20. Supersymmetry and Supergravity
Chapter 21. Superstrings
References
Field Theory
Gauge Theories
Particle Physics
Critical and Non-Perturbative Phenomena
Supergravity
Superstrings
Index
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