Effective field theories:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, VIC, Australia ; New Delhi, India ; Singapore
Cambridge University Press
2022
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | x, 613 Seiten Illustrationen, Diagramme |
| ISBN: | 9781108476980 |
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| 245 | 1 | 0 | |a Effective field theories |c Ulf-G. Meißner (Bonn University and Forschungszentrum Jülich), Akaki Rusetsky (Bonn University) |
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Record in the Search Index
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| adam_text |
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 04-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 References page ix 1 1 2 13 17 18 23 28 35 38 42 46 52 59 60 61 62 66 66 67 73 76 81 91 94 99 105 116 121 143 153 154
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 References 4 Low-Energy Effedive Field Theory of QCD 4.1 Introduction 4.2 The ¿’-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 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 Tree-Level Calculations Chiral Perturbation Theory at One Loop Chiral Lagrangian with Nucleons Consistent Formulations of Baryon Chiral Perturbation Theory Theoretical Uncertainties The Meaning of Low-Energy Theorems Including Electromagnetic and Weak Interactions Splitting of the Strong and the Electromagnetic Interactions Wess-Zumino-Witten Effective Action The η'-Meson and Large-Nc СҺРТ Invariance of the СҺРТ Lagrangian 161 161 162 169 170 174 176 180 188 192 197 204 205 219 224 236 238 242 245 247 252
256 257 263 263 265 275 277 291 299 304 309 316 337 346 370 373 378 402 408 413 421
vii Contents 4.19 Partially Quenched СҺРТ 4.20 The Θ-Term, Strong CP Violation and Axions 4.21 Literature Guide References 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 References 424 431 448 450 466 466 467 476 487 499 506 513 522 528 533 542 556 558 6 Exercises 565 Appendix A Notations and Conventions A.l Units and Metric A.2 Pauli Matrices A.3 Gell-Mann Matrices A.4 Dirac Matrices A.5 Isospin and 517(3) Flavor Symmetry A.6 Spherical Harmonics A.7 Clebsch-Gordan Coefficients A.8 Bessel Functions 599 Index 606 599 600 601 602 602 603 604 605 |
| adam_txt |
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 04-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 References page ix 1 1 2 13 17 18 23 28 35 38 42 46 52 59 60 61 62 66 66 67 73 76 81 91 94 99 105 116 121 143 153 154
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 References 4 Low-Energy Effedive Field Theory of QCD 4.1 Introduction 4.2 The ¿’-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 4.9 4.10 4.11 4.12 4.13 4.14 4.15 4.16 4.17 4.18 Tree-Level Calculations Chiral Perturbation Theory at One Loop Chiral Lagrangian with Nucleons Consistent Formulations of Baryon Chiral Perturbation Theory Theoretical Uncertainties The Meaning of Low-Energy Theorems Including Electromagnetic and Weak Interactions Splitting of the Strong and the Electromagnetic Interactions Wess-Zumino-Witten Effective Action The η'-Meson and Large-Nc СҺРТ Invariance of the СҺРТ Lagrangian 161 161 162 169 170 174 176 180 188 192 197 204 205 219 224 236 238 242 245 247 252
256 257 263 263 265 275 277 291 299 304 309 316 337 346 370 373 378 402 408 413 421
vii Contents 4.19 Partially Quenched СҺРТ 4.20 The Θ-Term, Strong CP Violation and Axions 4.21 Literature Guide References 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 References 424 431 448 450 466 466 467 476 487 499 506 513 522 528 533 542 556 558 6 Exercises 565 Appendix A Notations and Conventions A.l Units and Metric A.2 Pauli Matrices A.3 Gell-Mann Matrices A.4 Dirac Matrices A.5 Isospin and 517(3) Flavor Symmetry A.6 Spherical Harmonics A.7 Clebsch-Gordan Coefficients A.8 Bessel Functions 599 Index 606 599 600 601 602 602 603 604 605 |
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| author | Meißner, Ulf-G. 1957- Rusetsky, Akaki ca. 20./21. Jh |
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| isbn | 9781108476980 |
| language | English |
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| spelling | Meißner, Ulf-G. 1957- Verfasser (DE-588)118849323X aut Effective field theories Ulf-G. Meißner (Bonn University and Forschungszentrum Jülich), Akaki Rusetsky (Bonn University) Cambridge, United Kingdom ; New York, NY, USA ; Port Melbourne, VIC, Australia ; New Delhi, India ; Singapore Cambridge University Press 2022 x, 613 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Literaturangaben bicssc Quantenfeldtheorie (DE-588)4047984-5 gnd rswk-swf Effektive Theorie (DE-588)4560327-3 gnd rswk-swf Chirale Störungstheorie (DE-588)4618818-6 gnd rswk-swf Quantenchromodynamik (DE-588)4128082-9 gnd rswk-swf Effektive Theorie (DE-588)4560327-3 s Quantenfeldtheorie (DE-588)4047984-5 s Quantenchromodynamik (DE-588)4128082-9 s Chirale Störungstheorie (DE-588)4618818-6 s DE-604 Rusetsky, Akaki ca. 20./21. Jh. Verfasser (DE-588)1270517880 aut Erscheint auch als Online-Ausgabe, individual 978-1-108-75113-1 Erscheint auch als Online-Ausgabe, institutional 978-1-108-68903-8 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033797449&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Meißner, Ulf-G. 1957- Rusetsky, Akaki ca. 20./21. Jh Effective field theories bicssc Quantenfeldtheorie (DE-588)4047984-5 gnd Effektive Theorie (DE-588)4560327-3 gnd Chirale Störungstheorie (DE-588)4618818-6 gnd Quantenchromodynamik (DE-588)4128082-9 gnd |
| subject_GND | (DE-588)4047984-5 (DE-588)4560327-3 (DE-588)4618818-6 (DE-588)4128082-9 |
| title | Effective field theories |
| title_auth | Effective field theories |
| title_exact_search | Effective field theories |
| title_exact_search_txtP | Effective field theories |
| title_full | Effective field theories Ulf-G. Meißner (Bonn University and Forschungszentrum Jülich), Akaki Rusetsky (Bonn University) |
| title_fullStr | Effective field theories Ulf-G. Meißner (Bonn University and Forschungszentrum Jülich), Akaki Rusetsky (Bonn University) |
| title_full_unstemmed | Effective field theories Ulf-G. Meißner (Bonn University and Forschungszentrum Jülich), Akaki Rusetsky (Bonn University) |
| title_short | Effective field theories |
| title_sort | effective field theories |
| topic | bicssc Quantenfeldtheorie (DE-588)4047984-5 gnd Effektive Theorie (DE-588)4560327-3 gnd Chirale Störungstheorie (DE-588)4618818-6 gnd Quantenchromodynamik (DE-588)4128082-9 gnd |
| topic_facet | bicssc Quantenfeldtheorie Effektive Theorie Chirale Störungstheorie Quantenchromodynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033797449&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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