Effective field theories / Ulf-G. Meissner, Akaki Rusetsky.

Format:

Book

Author/Creator:

Meissner, Ulf-G., author.

Rusetsky, Akaki, author.

Language:

English

Subjects (All):

Quantum chromodynamics.

Quantum field theory.

Field theory (Physics).

Physical Description:

1 online resource (x, 613 pages) : digital, PDF file(s).

Edition:

First edition.

Place of Publication:

Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2022.

Summary:

Effective field theories are a widely used tool in various branches of physics. This book provides a comprehensive discussion of the foundations and fundamentals of effective field theories of quantum chromodynamics (QCD) in the light quark sector with an emphasis on the study of flavour symmetries and their realizations. In this context, different types of effective field theories pertaining to various energy scales are considered and selected applications are devised. It also covers the formulation of effective field theories in a finite volume and its application in the analysis of lattice QCD data. Effective Field Theories is intended for graduate students and researchers in particle physics, hadron physics and nuclear physics. Exercises are included to help the reader deepen their understanding of the topics discussed throughout, with solutions available to lecturers.

Contents:

Cover

Half-title Page

Title Page

Copyright Page

Contents

Preface

1 Basic Concepts

1.1 Introduction

1.2 Warm-up: Effective Theory for Scattering on the Potential Well

1.3 Integrating out a Heavy Scale: a Model at Tree Level

1.4 The Model at Tree Level: Path-Integral Formalism

1.5 Equations of Motion and Field Redefinitions

1.6 Light Particle Mass at One Loop

1.7 Matching of the Quartic Coupling at One Loop

1.8 Dependence of the Effective Couplings on the Heavy Mass

1.9 Decoupling in Different Renormalization Schemes

1.10 Floating Cutoff

1.11 Emergent Symmetries

1.12 Triviality of the ɸ[sup(4)]-Theory

1.13 Relevant Degrees of Freedom at Low Momenta

1.14 Construction Principles of an EFT

1.15 Literature Guide

References

2 Nonrelativistic Effective Theories

2.1 Introduction

2.2 Foldy-Wouthuysen Transformation

2.3 Construction of the Nonrelativistic Lagrangian for a Scalar Field

2.4 Symmetries

2.5 Perturbation Theory, Matching and the Effective Range Expansion

2.6 Nucleon-Nucleon Scattering: the Case of a Large Scattering Length

2.7 Relativistic Kinematics: Two-Particle Processes

2.8 Cusps in Three-Particle Decays

2.9 Dimers and the Faddeev Equation

2.10 Efimov Effect

2.11 Including Virtual Photons in Nonrelativistic Theories

2.12 Spectrum and Decays of Hadronic Atoms

2.13 Literature Guide

3 Symmetries

3.1 Introduction

3.2 Euler-Heisenberg Lagrangian

3.3 Interaction of Long-Wavelength Photons with Atoms

3.4 QCD Factsheet

3.5 Chiral Symmetry in QCD

3.6 Ward Identities

3.7 The Triangle Anomaly

3.8 Anomalies: Point-Split Technique

3.9 Fujikawa Determinant

3.10 Non-Abelian Anomalies

3.11 Atiyah-Singer Index Theorem

3.12 Chiral Symmetry and Anomalies on the Lattice.

3.13 Trace Anomaly, Dimensional Transmutation and the Proton Mass

3.14 Low-Energy Spectrum of QCD: Goldstone Theorem

3.15 Vafa-Witten Theorem

3.16 Quark Mass Dependence of Hadron Masses

3.17 Soft-Pion Technique

3.18 Witten-Veneziano Formula

3.19 Anomaly Matching

3.20 Symmetries and Spectrum of (Partially) Quenched QCD

3.21 Literature Guide

4 Low-Energy Effective Field Theory of QCD

4.1 Introduction

4.2 The S-Matrix of Composite Particles

4.3 Weinberg's Theorem

4.4 The σ-Model

4.5 The σ-Model with Nucleons

4.6 Nonlinear Realization of Chiral Symmetry

4.7 Chiral Perturbation Theory in the Meson Sector: Lagrangian and Generating Functional

4.8 Tree-Level Calculations

4.9 Chiral Perturbation Theory at One Loop

4.10 Chiral Lagrangian with Nucleons

4.11 Consistent Formulations of Baryon Chiral Perturbation Theory

4.12 Theoretical Uncertainties

4.13 The Meaning of Low-Energy Theorems

4.14 Including Electromagnetic and Weak Interactions

4.15 Splitting of the Strong and the Electromagnetic Interactions

4.16 Wess-Zumino-Witten Effective Action

4.17 The ղ[sup(')]-Meson and Large-N[sub(c)] ChPT

4.18 Invariance of the ChPT Lagrangian

4.19 Partially Quenched ChPT

4.20 The θ-Term, Strong CP Violation and Axions

4.21 Literature Guide

5 Effective Theories in a Finite Volume

5.1 Introduction

5.2 The Mass of a Stable Particle in a Finite Volume

5.3 Scattering States: the Lüscher Equation

5.4 Moving Frames, Angular Momentum and Spin

5.5 Twisted Boundary Conditions

5.6 Two-Particle Decays

5.7 Multiparticle Systems: Perturbative Expansion for the Energy Levels

5.8 Three-Particle Quantization Condition

5.9 Three-Particle Decays on the Lattice

5.10 Photons in a Finite Volume

5.11 The Chiral Limit in a Finite Volume.

5.12 Literature Guide

6 Exercises

Appendix A Notations and Conventions

A.1 Units and Metric

A.2 Pauli Matrices

A.3 Gell-Mann Matrices

A.4 Dirac Matrices

A.5 Isospin and SU(3) Flavor Symmetry

A.6 Spherical Harmonics

A.7 Clebsch-Gordan Coefficients

A.8 Bessel Functions

Index.

Notes:

Title from publisher's bibliographic system (viewed on 02 Nov 2022).

Includes bibliographical references and index.

ISBN:

9781108751131

110875113X

9781108689038

1108689035