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E-grāmata: Effective Field Theories

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(Rheinische Friedrich-Wilhelms-Universitat Bonn and Forschungszentrum Jülich), (Rheinische Friedrich-Wilhelms-Universität Bonn)
  • Formāts: PDF+DRM
  • Izdošanas datums: 25-Aug-2022
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781108751131
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Effective Field TheoriesPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 25-Aug-2022
  • Izdevniecība: Cambridge University Press
  • Valoda: eng
  • ISBN-13: 9781108751131
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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.

Effective field theories are a widely used tool in various branches of physics. Intended for graduate students and researchers, this book focuses on the effective field theories of the strong interactions in the light quark sector and connects them to forefront investigations.

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A detailed and comprehensive exploration of the foundations and fundamentals of effective field theories.
Preface ix
1 Basic Concepts
1(65)
1.1 Introduction
1(1)
1.2 Warm-up: Effective Theory for Scattering on the Potential Well
2(11)
1.3 Integrating out a Heavy Scale: a Model at Tree Level
13(4)
1.4 The Model at Tree Level: Path-Integral Formalism
17(1)
1.5 Equations of Motion and Field Redefinitions
18(5)
1.6 Light Particle Mass at One Loop
23(5)
1.7 Matching of the Quartic Coupling at One Loop
28(7)
1.8 Dependence of the Effective Couplings on the Heavy Mass
35(3)
1.9 Decoupling in Different Renormalization Schemes
38(4)
1.10 Floating Cutoff
42(4)
1.11 Emergent Symmetries
46(6)
1.12 Triviality of the Φ4-Theory
52(7)
1.13 Relevant Degrees of Freedom at Low Momenta
59(1)
1.14 Construction Principles of an EFT
60(1)
1.15 Literature Guide
61(5)
References
62(4)
2 Nonrelativistic Effective Theories
66(95)
2.1 Introduction
66(1)
2.2 Foldy--Wouthuysen Transformation
67(6)
2.3 Construction of the Nonrelativistic Lagrangian for a Scalar Field
73(3)
2.4 Symmetries
76(5)
2.5 Perturbation Theory, Matching and the Effective Range Expansion
81(10)
2.6 Nucleon--Nucleon Scattering: the Case of a Large Scattering Length
91(3)
2.7 Relativistic Kinematics: Two-Particle Processes
94(5)
2.8 Cusps in Three-Particle Decays
99(6)
2.9 Dimers and the Faddeev Equation
105(11)
2.10 Efimov Effect
116(5)
2.11 Including Virtual Photons in Nonrelativistic Theories
121(22)
2.12 Spectrum and Decays of Hadronic Atoms
143(10)
2.13 Literature Guide
153(8)
References
154(7)
3 Symmetries
161(102)
3.1 Introduction
161(1)
3.2 Euler--Heisenberg Lagrangian
162(7)
3.3 Interaction of Long-Wavelength Photons with Atoms
169(1)
3.4 QCD Factsheet
170(4)
3.5 Chiral Symmetry in QCD
174(2)
3.6 Ward Identities
176(4)
3.7 The Triangle Anomaly
180(8)
3.8 Anomalies: Point-Split Technique
188(4)
3.9 Fujikawa Determinant
192(5)
3.10 Non-Abelian Anomalies
197(7)
3.11 Atiyah--Singer Index Theorem
204(1)
3.12 Chiral Symmetry and Anomalies on the Lattice
205(14)
3.13 Trace Anomaly, Dimensional Transmutation and the Proton Mass
219(5)
3.14 Low-Energy Spectrum of QCD: Goldstone Theorem
224(12)
3.15 Vafa--Witten Theorem
236(2)
3.16 Quark Mass Dependence of Hadron Masses
238(4)
3.17 Soft-Pion Technique
242(3)
3.18 Witten--Veneziano Formula
245(2)
3.19 Anomaly Matching
247(5)
3.20 Symmetries and Spectrum of (Partially) Quenched QCD
252(4)
3.21 Literature Guide
256(7)
References
257(6)
4 Low-Energy Effective Field Theory of QCD
263(203)
4.1 Introduction
263(2)
4.2 The S-Matrix of Composite Particles
265(10)
4.3 Weinberg's Theorem
275(2)
4.4 The σ-Model
277(14)
4.5 The σ-Model with Nucleons
291(8)
4.6 Nonlinear Realization of Chiral Symmetry
299(5)
4.7 Chiral Perturbation Theory in the Meson Sector: Lagrangian and Generating Functional
304(5)
4.8 Tree-Level Calculations
309(7)
4.9 Chiral Perturbation Theory at One Loop
316(21)
4.10 Chiral Lagrangian with Nucleons
337(9)
4.11 Consistent Formulations of Baryon Chiral Perturbation Theory
346(24)
4.12 Theoretical Uncertainties
370(3)
4.13 The Meaning of Low-Energy Theorems
373(5)
4.14 Including Electromagnetic and Weak Interactions
378(24)
4.15 Splitting of the Strong and the Electromagnetic Interactions
402(6)
4.16 Wess--Zumino--Witten Effective Action
408(5)
4.17 The η'-Meson and Large-Nc. ChPT
413(8)
4.18 Invariance of the ChPT Lagrangian
421(3)
4.19 Partially Quenched ChPT
424(7)
4.20 The θ-Term, Strong CP Violation and Axions
431(17)
4.21 Literature Guide
448(18)
References
450(16)
5 Effective Theories in a Finite Volume
466(99)
5.1 Introduction
466(1)
5.2 The Mass of a Stable Particle in a Finite Volume
467(9)
5.3 Scattering States: the Luscher Equation
476(11)
5.4 Moving Frames, Angular Momentum and Spin
487(12)
5.5 Twisted Boundary Conditions
499(7)
5.6 Two-Particle Decays
506(7)
5.7 Multiparticle Systems: Perturbative Expansion for the Energy Levels
513(9)
5.8 Three-Particle Quantization Condition
522(6)
5.9 Three-Particle Decays on the Lattice
528(5)
5.10 Photons in a Finite Volume
533(9)
5.11 The Chiral Limit in a Finite Volume
542(14)
5.12 Literature Guide
556(9)
References
558(7)
6 Exercises
565(34)
Appendix A Notations and Conventions
599(7)
A.1 Units and Metric
599(1)
A.2 Pauli Matrices
600(1)
A.3 Gell--Mann Matrices
601(1)
A.4 Dirac Matrices
602(1)
A.5 Isospin and SU(3) Flavor Symmetry
602(1)
A.6 Spherical Harmonics
603(1)
A.7 Clebsch--Gordan Coefficients
604(1)
A.8 Bessel Functions
605(1)
Index 606
Ulf-G Meißner is Professor in Theoretical Physics at Bonn University, Germany and Director at the Institute for Advanced Simulation, Forschungszentrum Jülich, Germany. His research focuses on strong interaction physics, especially nuclear and particle physics. He was awarded the Lise-Meitner prize of the European Physical Society and the Distinguished Scientist Award of the Chinese Academy of Sciences. Akaki Rusetsky works at the Helmholtz Institute for Radiation and Nuclear Physics at Bonn University, Germany. His research focuses on strong interaction physics, effective field theories and lattice field theories. He received the Visiting Scientist award under the Chinese Academy of Sciences President's International Fellowship Initiative.
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