Quantum Field Theory
Weinberg, The Quantum Theory of Fields
Weinberg's QFT textbook is both a bible and a Pandora's box.
It is said that just reading it can bring both enlightenment and pain.
Read this first.
Peskin&Schroeder, An Introduction to Quantum Field Theory
[2] Klein-Gordon Field Quantization
[3] Dirac Field Quantization
[4] Perturbation
[7,10] QED Renormalization
[9,16] Path Integral Quantization
[11,12] Renormalization Group
[16] QCD Renormalization
[6,18] Vertex Operator
[9,19] Ward Identity and Anomaly
[16,19] Asymptotic Freedom and Trace Anomaly
1. Historical Introduction
1.1 Relativistic Wave Mechanics
1.2 The Birth of Quantum Field Theory
1.3 The Problems of Infinities
2. Relativistic Quantum Mechanics
2.3 Quantum Lorentz Transformations
2.5 One-Particle States
2.6 Space Inversion and Time-Reversal
2.7 Projective Representations
2. Appendix A The Symmetry Representation Theorem
2. Appendix B Group Operators and Homotopy Classes
2. Appendix C Inversions and Degenerate Multiplets
2. Problems
3. Scattering Theory
3.1 'In' and 'Out' States
3.2 The $S$-matrix
3.3 Symmetries of the $S$-Matrix
3.4 Rates and Cross-Sections
3.5 Perturbation Theory
3.6 Implications of Unitary
3.7 Partial-Wave Expansions
3.8 Resonance
3. Problems
4. The Cluster Decomposition Principle
4.1 Bosons and Fermions
4.2 Creation and Annihilation Operators
4.3 Cluster Decomposition and Connected Amplitudes
4.4 Structure of the Interaction
4. Problems
5. Quantum Fields and Antiparticles
5.1 Free Fields
5.2 Causal Scalar Fields
5.3 Causal Vector Fields
5.4 The Dirac Formalism
5.5 Causal Dirac Fields
5.6 General Irreducible Representations of the Homogeneous Lorentz Group
5.7 General Causal Fields
5.8 The $CPT$ Theorem
5.9 Massless Particle Fields
5. Problems
6. The Feynman Rules
6.1 Derivation of the Rules
6.2 Calculation of the Propagator
6.3 Momentum Spce Rules
6.4 Off the Mass Shell
6. Problems
7. The canonical Formalism
7.1 Canonical Variables
7.2 The Lagrangian Formalism
7.3 Global Symmetries
7.4 Lorentz Invariance
7.5 Transition to Interaction Picture: Examples
7.6 Constraints and Dirac Brackets
7.7 Field Redefinitions and Redundant Couplings
7. Appendix Dirac Brackets from Canonical Commutators
7. Problems
8. Electrodynamics
8.1 Gauge Invariance
8.2 Constraints and Gauge Conditions
8.3 Quantization in Coulomb Gauge
8.4 Electrodynamics in the Interaction Picture
8.5 The Photon Propagator
8.6 Feynman Rules for Spinor Electrodynamics
8.7 Compton Scattering
8.8 Generalization: $p$-form gauge Fields
8. Appendix Traces
8. Problems
9. Path-Integral Methods
9.1 The General Path-integral Formula
9.2 Transiton to the $S$-Matrix
9.3 Lagrangian Version of the Path-Integral Formula
9.4 Path-Integral Derivation of Feynman Rules
9.5 Path Integrals for Fermions
9.6 Path-Integral Formulation of QUantum Electrodynamics
9.7 Varieties of Statistics
9. Appendix Gaussian Multiple Integrals
9. Problems
10. Non-Perturbative Methods
10.1 Symmetries
10.2 Pology
10.3 Fields and Mass Renormalization
10.4 Renormalized Cahrge and Ward Identities
10.5 Gauge Invariance
10.6 Electromagnetic Form Factors and Magnetic Moment
10.7 The Kallen-Lehmann Representation
10.8 Dispersion Relations
10. Problems
11. One-Loop Radiative Correnctions in QUantum Electrodynamics
11.1 Counterterms
11.2 Vacuum Polarization
11.3 Anomalous Magnetic Moments and Charge Radii
11.4 Electron Self-Energy
11.Appendix Assorted Ingerals
11. Problems
12. General Renormalization Theory
12.1 Degrees of Divergence
12.2 Cancellation of Divergences
12.3 Is Renormalizability Necessary?
12.4 The Floating Cutoff
12.5 Accidental Symmetries
12. Problems
13. Infrared Effects
13.1 Soft Photon Amplitudes
13.2 Virtual Soft Photons
13.3 Real Soft Photons; Cancellation of Divergences
13.4 General Infrared Divergences
13.5 Soft Photon Scattering
13.6 The External Field Approximation
13. Problems
14. Bound States in External Fields
14.1 The Dirac Equation
14.2 Radiative Corrections in External Fields
14.3 The Lamb Shift in Light Atoms
14. Problems
15. Non-Ableian Gauge Theories
15.2 Gauge Theory Lagrangians and Simple Lie Groups
15.3 Fields Equations and Conservation Laws
15.4 Quantization
15.5 The De Witt-Faddeev-Popov Method
15.6 Ghosts
15.7 BRST Symmetry
15.8 Generalizations of BRST Symmetry
15.9 The Batalin-Vilkovisky Formalism
15. Appendix A A Theorem Regarding Lie Algebras
15. Appendix B The Cartan Catalog
Problems
16. External Field Methods
16.1 The Quantum Effective Action
16.2 Calculation of the Effective Potential
16.3 Energy Interpretation
16.4 Symmetries of the Effective Action
16. Problems
17. Renormalization of Gauge Theories
17.1 The Zinn-Justin Equation
17.2 Renormalization: Direct Analysis
17.3 Renormalization: General Gauge Theories
17.4 Background Field Gauge
17.5 A One-Loop Calculation in Background Field Gauge
17. Problems
18. Renormalization Group Methods
18.1 Where do the Large Logarithms Come From?
18.2 The Sliding Scale
18.3 Varieties of Asymptotic Behavior
18.4 Multiple Couplings and Mass Effects
18.5 Critical Phenomena
18.6 Minimal Subtraction
18.7 Quantum Chromodynamics
18.8 Improved Perturbation Theory
18. Problems
19. Spontaneously Broken Global Symmetries
19.1 Degenerate Vacua
19.2 Goldstone Bosons
19.3 Spontaneously Broken Approximate Symmetries
19.4 Pions as Goldstone Bosons
19.5 Effective Field Theories: Pions and Nucleons
19.6 Effective Field Theories: General Broken Symmetries
19.7 Effective Field Theories: $SU(3)\times SU(3)$
19.8 Anomalous Terms in Effective Field Theories
19.9 Unbroken Symmetries
19.10 The $U(1)$ Problem
19. Problems
20. Operator Product Expansions
20.1 The Expansion: Dscription and Derivation
20.2 Momentum Flow
20.3 Renormalization Group Equations for Coefficient Functions
20.4 Symmetry Properties of Coefficient Functions
20.5 Spectral Function Sum Rules
20.6 Deep Inelastic Scattering
20.7 Renormalous
20. Appendix Momentum Flow: The General Case
Problems
21. Spontatneously Broken Gauge Symmetries
21.1 Unitarity Gauge
21.2 Renormalizable $\zeta$-Gauges
21.3 The Electroweak Theory
21.4 Dynamically Broken Local Symmetries
21.5 Electroweak-Strong Unification
21.6 Superconductivity
21. Appendix General Unitarity Gauge
21. Problems
22. Anomalies
22.1 The $\pi^0$ Decay Problem
22.2 Transformation of the Measure: The Abelian Anomaly
22.3 Direct Calculation of Anomalies: The General Case
22.4 Anomaly-Free Gauge Theories
22.5 Massless Bound States
22.6 Consistency Conditions
22.7 Anomalies and Goldstone Bosons
22. Problems
23. Extended Field Configurations
23.1 The Uses of Topology
23.2 Homotopy Groups
23.3 Monopoles
23.4 The Cartan-Manrer Integral Invariant
23.5 Instantons
23.6 The Theta Angle
23.7 Quantum Fluctuations around Extended Field Configurations
23.8 Vacuum Deccay
23. Appendix A Euclidean Path Integrals
23. Appendix B A List of Homotopy Group
23. Problems
24. Historical Introduction
24.1 Unconventional Symmetries and 'No-Go' Theorems
24.2 The Birth of Supersymmetry
24. Appendix A $SU(6)$ Symmetry of Non-Relativistic Quark Models
24. Appendix B The Colman-Mandula Theorem
24. Problems
25. Supersymmetry Algebras
25.1 Graded Lie Algebras and Graded Parameters
25.2 Supersymmetry Algebras
25.3 Space Inversion Properties of Supersymmetry Generators
25.4 Massless Particle Supermultiplets
25.5 Massive Particle Supermultiplets
25. Problems
26. Supersymmetry Field Theories
26.1 Direct Construction of Field Supermultiplets
26.2 General Superfields
26.3 Chiral and Linear Superfields
26.4 Renormalizable Theoreis of Chiral Superfields
26.5 Spontatneous Supersymmetry Breaking in the Tree Approximation
26.6 Superspace Integrals, Field Equations, and the Current Superfield
26.7 The Supercurrent
26.8 General Kahler Potentials
26. Appendix Majorana Spinors
26. Problems
27. Supersymmetric Gauge Theories
27.1 Gauge-Invariant Actions for Chiral Superfields
27.2 Gauge-Invariant Action for Abelian Gauge Superfileds
27.3 Gauge-Invariant Action for General Gauge Superfields
27.4 Renormalizable Gauge Theoreis with Chiral Superfields
27.5 Supersymmetry Breaking in the Tree Approximation Resumed
27.6 Perturbative Non-Renormalization Theorems
27.7 Soft Supersymmetry Breaking
27.8 Another Approach: Gauge-Invariant Supersymmetry Transformations
27.9 Gauge Theories with Extended Supersymmetry
27. Problems
28. Supersymmetric Versions of the Standard Model
28.1 Superfields, Anomalies, and Conservation Laws
28.2 Supersymmetry and Strong-Electroweak Unification
28.3 Where is Supersymmetry Broken?
28.4 The Minomal Supersymmetric Standard Model
28.5 The Sector of Zero Baryon and Lepton Number\
28.6 Gauge Mediation of Supersymmetry Breaking
28.7 Baryon and Lepton Non-Conservation
28. Problems
29. Beyond Perterbation Theory
29.1 General Aspects of Supersymmetry Breaking
29.2 Supersymmetry Current Sum Rules
29.3 Non-Perturbative Corrections to the Superpotential
29.4 Supersymmetry Breaking in Gauge Theories
29.5 The Seiberg-Witten Solution
29. Problems
30. Supergraphs
30.1 Potential Superfields
30.2 Superpropagators
30.3 Calculations with Supergraphs
30. Problems
31. Supergravity
31.1 The Metric Superfield
31.2 The Gravitational Action
31.3 The Gravitino
31.4 Anomaly-Mediated Supersymmetry Breaking
31.5 Local Supersymmetry Transformations
31.6 Supergravity to All Orders
31.7 Gravity-Mediated Supersymmetry Breaking
31. Appendix The Vierbein Formalism
31. Problems
32. Supersymmetry Algebras in Higher Dimensions
32.1 General Supersymmetry Algebras
32.2 Massless Multiplets
32.3 $p$-Branes
32. Appendix Spinors in Higher Dimentions
32. problems
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QFT is general tools for describe unknown system.