Effective Lagrangians for the Standard Model

1. The Notion of Effective Lagrangian.- 1.1 Introduction.- 1.2 Integration of the Heavy Modes.- 1.2.1 The Effective Action for the Light Modes.- 1.2.2 Low Energy Expansions.- 1.3 The Decoupling Theorem.- 1.4 The Euler-Heisenberg Lagrangian.- 1.5 Theories with Spontaneous Symmetry Breaking.- 1.6 Decoupling of Chiral Fermions.- 1.7 References.- 2. Global Symmetries in Quantum Field Theory.- 2.1 Classical Symmetries.- 2.2 Green Functions and the Reduction Formula.- 2.3 Quantum Symmetries and Ward Identities.- 2.4 Spontaneous Symmetry Breaking and the Goldstone Theorem.- 2.5 Explicit Symmetry Breaking and the Dashen Conditions.- 2.6 References.- 3. The Non-linear ? Model.- 3.1 Introduction.- 3.2 The Geometry and the Dynamics of the Non-linear ? Model.- 3.3 The Quantum Non-linear ? Model.- 3.4 Reparametrization Invariance of the S-Matrix Elements.- 3.5 Local Symmetries and the Higgs Mechanism.- 3.6 Topologically Non-trivial Configurations.- 3.7 References.- 4. Anomalies.- 4.1 Introduction.- 4.2 The Axial Anomaly, Triangle Diagrams and the ?0 Decay.- 4.3 The Axial Anomaly and the Index Theorem.- 4.4 Gauge Anomalies.- 4.4.1 The Wess-Zumino Consistency Conditions.- 4.5 Regularization Methods.- 4.6 Ambiguities and Counterterms.- 4.7 Topological Interpretation of Non-Abelian Anomalies.- 4.8 Non-perturbative Anomalies.- 4.9 Non-linear ? Model Anomalies.- 4.10 The Wess-Zumino-Witten Term.- 4.10.1 Anomalous Processes in QCD.- 4.10.2 The Non-local Anomalous Effective Action.- 4.10.3 The WZW Term with Gauge Fields.- 4.10.4 Anomalous Processes and the WZW Term.- 4.10.5 The SU(2) WZW Term.- 4.11 The Trace Anomaly.- 4.12 References.- 5. The Symmetries of the Standard Model.- 5.1 The Elements of the Standard Model.- 5.1.1 Matter.- 5.1.2 Gauge Fields.- 5.1.3 The Symmetry Breaking Sector.- 5.2 The Cabibbo-Kobayashi-Maskawa Matrix and Weak CP Violation.- 5.3 The Cancellation of Gauge Anomalies in the Standard Model.- 5.4 Baryon and Lepton Number Anomalies in the Standard Model.- 5.5 The Evolution of the Coupling Constants.- 5.6 The Strong CP Problem.- 5.6.1 The ?-Vacuum.- 5.6.2 The Role of Instantons.- 5.6.3 The Strong CP Problem.- 5.7 The Symmetries of the Standard Model.- 5.8 References.- 6. The Effective Lagrangian for QCD.- 6.1 The QCD Lagrangian.- 6.2 QCD at Low Energies.- 6.3 The Chiral Lagrangian at Leading Order.- 6.4 The Chiral Lagrangian to Next to Leading Order.- 6.4.1 The L(4) Lagrangian.- 6.4.2 One-Loop Renormalization.- 6.4.3 The Effective Action to One Loop.- 6.5 The Low-Energy Constants.- 6.5.1 Phenomenological Estimates.- 6.5.2 Theoretical Estimates.- 6.5.3 The Nf = 2 Case.- 6.6 The Problem of Unitarity in ChPT.- 6.6.1 Unitarity and Dispersion Relations.- 6.6.2 The Large-N Limit.- 6.7 References.- 7. The Standard Model Symmetry Breaking Sector.- 7.1 The Mass Problem.- 7.2 The Effective Lagrangian for the SM Symmetry Breaking Sector.- 7.3 The O(p4) Lagrangian and One-Loop Renormalization.- 7.3.1 The 0(p4) Lagrangian.- 7.3.2 The Covariant Formalism.- 7.3.3 One-Loop Renormalization.- 7.4 The Heavy Higgs and QCD-Like Models.- 7.4.1 The Heavy Higgs Model.- 7.4.2 QCD-Like Models.- 7.5 Phenomenological Determination of the Chiral Parameters.- 7.5.1 Precision Tests of the Standard Model (Oblique Corrections).- 7.5.2 The Trilinear Gauge Boson Vertex.- 7.5.3 Elastic Gauge Boson Scattering.- 7.6 The Equivalence Theorem.- 7.6.1 Introduction.- 7.6.2 The Slavnov-Taylor Identities.- 7.6.3 The Reduction Formula.- 7.6.4 The Generalized Equivalence Theorem.- 7.6.5 The Equivalence Theorem.- 7.7 The Applicability of the Equivalence Theorem.- 7.8 Gauge Boson Scattering at High Energies.- 7.8.1 Dispersion Relations for the SM Symmetry Breaking Sector.- 7.8.2 The Large-N Limit: The Higgs and the General Case.- 7.9 References.- 8. Gravity and the Standard Model.- 8.1 Introduction.- 8.2 The Standard Model in Curved Space-Time.- 8.3 Anomalies in the Standard Model.- 8.3.1 The Leptonic and Baryonic Anomalies.- 8.3.2 Gauge Anomalies.- 8.3.3 Gravitational A...