Effective Lagrangians for the Standard Model

This book will be useful for graduate students as well as particle physicists, from those who are just willing to obtain an overview of these subjects, up to those who want to start doing research.

Klappentext

This book presents a detailed and pedagogical exposition of the effective Lagrangian techniques and their applications to high-energy physics. It covers the main theoretical ideas and describes comprehensively how to use them in different fields, such as chiral perturbation theory and the symmetry breaking sector of the standard model and even low-energy quantum gravity. The book is written in the language of modern quantum field theory. Some of the theoretical topics treated are: decoupling, the Goldstone theorem, the non-linear sigma model, anomalies, the Wess--Zumino--Witten term, and the equivalence theorem.

Inhalt

1. The Notion of Effective Lagrangian.- 1.1 Introduction.- 1.2 Integration of the Heavy Modes.- 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.- 4.5 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.- 4.11 The Trace Anomaly.- 4.12 References.- 5. The Symmetries of the Standard Model.- 5.1 The Elements of the Standard Model.- 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.- 5.7 The Symmetries of the Standard Model.- 5.8 References.- 6. The Effective Lagrangian for QCD.- 6.1 The QCD Lagrangian.- 6.2QCD at Low Energies.- 6.3 The Chiral Lagrangian at Leading Order.- 6.4 The Chiral Lagrangian to Next to Leading Order.- 6.5 The Low-Energy Constants.- 6.6 The Problem of Unitarity in ChPT.- 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.- 7.4 The Heavy Higgs and QCD-Like Models.- 7.5 Phenomenological Determination of the Chiral Parameters.- 7.6 The Equivalence Theorem.- 7.7 The Applicability of the Equivalence Theorem.- 7.8 Gauge Boson Scattering at High Energies.- 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.- 8.4 The Effect of Matter Fields on Gravitation.- 8.5 The Effective Action for Gravity.- 8.6 References.- A. Useful Formulae and Notation.- B. Notes on Differential Geometry.- C. Aspects of Quantum Field Theory.- D. Unitarity and Partial Waves.