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Introduction to Effective Field Theory: Thinking Effectively about Hierarchies of Scale [Hardback]

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  • Formāts: Hardback, 660 pages, height x width x depth: 260x183x34 mm, weight: 1520 g, Worked examples or Exercises
  • Izdošanas datums: 10-Dec-2020
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521195470
  • ISBN-13: 9780521195478
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Introduction to Effective Field Theory: Thinking Effectively about Hierarchies of ScalePalielināt
  • Formāts: Hardback, 660 pages, height x width x depth: 260x183x34 mm, weight: 1520 g, Worked examples or Exercises
  • Izdošanas datums: 10-Dec-2020
  • Izdevniecība: Cambridge University Press
  • ISBN-10: 0521195470
  • ISBN-13: 9780521195478
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780521195478.html
Keywords:
Using examples from across the sub-disciplines of physics, this introduction shows why effective field theories are the language in which physical laws are written. The tools of effective field theory are demonstrated using worked examples from areas including particle, nuclear, atomic, condensed matter and gravitational physics. To bring the subject within reach of scientists with a wide variety of backgrounds and interests, there are clear physical explanations, rigorous derivations, and extensive appendices on background material, such as quantum field theory. Starting from undergraduate-level quantum mechanics, the book gets to state-of-the-art calculations using both relativistic and nonrelativistic few-body and many-body examples, and numerous end-of-chapter problems derive classic results not covered in the main text. Graduate students and researchers in particle physics, condensed matter physics, nuclear physics, string theory, and mathematical physics more generally, will find this book ideal for both self-study and for organized courses on effective field theory.

Recenzijas

'This book can serve as a reference work for graduate students of theoretical physics as well as a professional reference Recommended.' M. O. Farooq, Choice

Papildus informācija

This advanced, accessible textbook on effective field theories uses worked examples to bring this important topic to a wider audience.
List of Illustrations
xi
List of Tables
xvii
Preface xix
Acknowledgements xxi
Part I Theoretical Framework
1(146)
1 Decoupling and Hierarchies of Scale
5(13)
1.1 An Illustrative Toy Model
6(3)
1.1.1 Semiclassical Spectrum
6(1)
1.1.2 Scattering
7(2)
1.1.3 The Low-Energy Limit
9(1)
1.2 The Simplicity of the Low-Energy Limit
9(7)
1.2.1 Low-Energy Effective Actions
10(1)
1.2.2 Why It Works
11(2)
1.2.3 Symmetries: Linear vs Nonlinear Realization
13(3)
1.3 Summary
16(2)
Exercises
16(2)
2 Effective Actions
18(33)
2.1 Generating Functionals -- A Review
18(8)
2.1.1 Connected Correlations
21(1)
2.1.2 The 1PI (or Quantum) Action
22(4)
2.2 The High-Energy/Low-Energy Split
26(6)
2.2.1 Projecting onto Low-Energy States
26(2)
2.2.2 Generators of Low-Energy Correlations
28(1)
2.2.3 The 1LPI Action
29(3)
2.3 The Wilson action
32(7)
2.3.1 Definitions
33(6)
2.4 Dimensional Analysis and Scaling
39(5)
2.4.1 Dimensional Analysis
39(4)
2.4.2 Scaling
43(1)
2.5 Redundant Interactions
44(4)
2.6 Summary
48(3)
Exercises
49(2)
3 Power Counting and Matching
51(31)
3.1 Loops, Cutoffs and the Exact RG
52(12)
3.1.1 Low-Energy Amplitudes
53(1)
3.1.2 Power Counting Using Cutoffs
54(5)
3.1.3 The Exact Renormalization Group
59(4)
3.1.4 Rationale behind Renormalization
63(1)
3.2 Power Counting and Dimensional Regularization
64(12)
3.2.1 EFTs in Dimensional Regularization
65(3)
3.2.2 Matching vs Integrating Out
68(3)
3.2.3 Power Counting Using Dimensional Regularization
71(3)
3.2.4 Power Counting with Fermions
74(2)
3.3 The Big Picture
76(3)
3.3.1 Low-Energy Theorems
76(1)
3.3.2 The Effective-Action Logic
77(2)
3.4 Summary
79(3)
Exercises
79(3)
4 Symmetries
82(34)
4.1 Symmetries in Field Theory
82(8)
4.1.1 Unbroken Continuous Symmetries
84(3)
4.1.2 Spontaneous Symmetry Breaking
87(3)
4.2 Linear vs Nonlinear Realizations
90(15)
4.2.1 Linearly Realized Symmetries
91(2)
4.2.2 Nonlinearly Realized Symmetries
93(6)
4.2.3 Gauge Symmetries
99(6)
4.3 Anomaly Matching
105(8)
4.3.1 Anomalies
105(3)
4.3.2 Anomalies and EFTs
108(5)
4.4 Summary
113(3)
Exercises
113(3)
5 Boundaries
116(10)
5.1 `Induced' Boundary Conditions
116(3)
5.2 The Low-Energy Perspective
119(3)
5.3 Dynamical Boundary Degrees of Freedom
122(1)
5.4 Summary
123(3)
Exercises
124(2)
6 Time-Dependent Systems
126(21)
6.1 Sample Time-Dependent Backgrounds
126(3)
6.1.1 View from the EFT
128(1)
6.2 EFTs and Background Solutions
129(8)
6.2.1 Adiabatic Equivalence of EFT and Full Evolution
129(3)
6.2.2 Initial Data and Higher-Derivative Instabilities
132(5)
6.3 Fluctuations about Evolving Backgrounds
137(7)
6.3.1 Symmetries in an Evolving Background
138(3)
6.3.2 Counting Goldstone States and Currents
141(3)
6.4 Summary
144(3)
Exercises
145(2)
Part II Relativistic Applications
147(126)
7 Conceptual Issues (Relativistic Systems)
151(37)
7.1 The Fermi Theory of Weak Interactions
151(4)
7.1.1 Properties of the W Boson
151(2)
7.1.2 Weak Decays
153(2)
7.2 Quantum Electrodynamics
155(14)
7.2.1 Integrating Out the Electron
156(6)
7.2.2 E >> me and Large Logs
162(2)
7.2.3 Muons and the Decoupling Subtraction Scheme
164(3)
7.2.4 Gauge/Goldstone Equivalence Theorems
167(2)
7.3 Photons, Gravitons and Neutrinos
169(8)
7.3.1 Renormalizable Interactions
169(2)
7.3.2 Strength of Non-renormalizable Interactions
171(2)
7.3.3 Neutrino-Photon Interactions
173(4)
7.4 Boundary Effects
177(8)
7.4.1 Surfaces between Media
178(4)
7.4.2 Casimir Energies
182(3)
7.5 Summary
185(3)
Exercises
186(2)
8 QCD and Chiral Perturbation Theory
188(24)
8.1 Quantum Chromodynamics
188(7)
8.1.1 Quarks and Hadrons
188(2)
8.1.2 Asymptotic Freedom
190(2)
8.1.3 Symmetries and Their Realizations
192(3)
8.2 Chiral Perturbation Theory
195(13)
8.2.1 Nonlinear Realization
195(4)
8.2.2 Soft-Pion Theorems
199(4)
8.2.3 Including Baryons
203(2)
8.2.4 Loops and Logs
205(3)
8.3 Summary
208(4)
Exercises
209(3)
9 The Standard Model as an Effective Theory
212(29)
9.1 Particle Content and Symmetries
213(8)
9.1.1 The Lagrangian
215(3)
9.1.2 Anomaly Cancellation
218(3)
9.2 Non-renormalizable Interactions
221(5)
9.2.1 Dimension-Five Interactions
222(2)
9.2.2 Dimension-Six Interactions
224(2)
9.3 Naturalness Issues
226(12)
9.3.1 Technical and 't Hooft Naturalness
226(5)
9.3.2 The Electroweak Hierarchy Problem
231(5)
9.3.3 The Cosmological Constant Problem
236(2)
9.4 Summary
238(3)
Exercises
239(2)
10 General Relativity as an Effective Theory
241(32)
10.1 Domain of Semi-Classical Gravity
243(4)
10.2 Time-Dependence and Cosmology
247(10)
10.2.1 Semiclassical Perturbation Theory
249(3)
10.2.2 Slow-Roll Suppression
252(5)
10.3 Turtles All the Way Down?
257(12)
10.3.1 String Theory
257(7)
10.3.2 Extra Dimensions
264(5)
10.4 Summary
269(4)
Exercises
270(3)
Part III Nonrelativistic Applications
273(114)
11 Conceptual Issues (Nonrelativistic Systems)
277(19)
11.1 Integrating Out Antiparticles
277(3)
11.2 Nonrelativistic Scaling
280(4)
11.2.1 Spinless Fields
280(2)
11.2.2 Spin-Half Fields
282(2)
11.3 Coupling to Electromagnetic Fields
284(9)
11.3.1 Scaling
285(4)
11.3.2 Power Counting
289(4)
11.4 Summary
293(3)
Exercises
294(2)
12 Electrodynamics of Nonrelativistic Particles
296(39)
12.1 Schrodinger from Wilson
296(11)
12.1.1 Leading Electromagnetic Interactions
296(2)
12.1.2 Matching
298(8)
12.1.3 Thomson Scattering
306(1)
12.2 Multiple Particle Species
307(19)
12.2.1 Atoms and the Coulomb Potential
309(2)
12.2.2 Dipole Approximation
311(3)
12.2.3 HQET
314(4)
12.2.4 Particle-Antiparticle Systems
318(8)
12.3 Neutral Systems
326(6)
12.3.1 Polarizability and Rayleigh Scattering
326(4)
12.3.2 Multipole Moments
330(2)
12.4 Summary
332(3)
Exercises
333(2)
13 First-Quantized Methods
335(52)
13.1 Effective Theories for Lumps
336(9)
13.1.1 Collective Coordinates
337(3)
13.1.2 Nonlinearly Realized Poincare Symmetry
340(4)
13.1.3 Other Localized Degrees of Freedom
344(1)
13.2 Point-Particle EFTs
345(8)
13.2.1 Electromagnetic Couplings
346(2)
13.2.2 Gravitational Couplings
348(1)
13.2.3 Boundary Conditions I
348(4)
13.2.4 Thomson Scattering Revisited
352(1)
13.3 PPEFT and Central Forces
353(27)
13.3.1 Boundary Conditions II
354(5)
13.3.2 Contact Interaction
359(6)
13.3.3 Inverse-Square Potentials: Fall to the Centre
365(5)
13.3.4 Nuclear Effects in Atoms
370(10)
13.4 Summary
380(7)
Exercises
381(6)
Part IV Many-Body Applications
387(127)
14 Goldstone Bosons Again
391(32)
14.1 Magnons
391(12)
14.1.1 Antiferromagnetism
392(5)
14.1.2 Ferromagnetism
397(4)
14.1.3 Physical Applications
401(2)
14.2 Low-Energy Superconductors
403(10)
14.2.1 Implications of the Goldstone Mode
404(6)
14.2.2 Landau-Ginzburg Theory
410(3)
14.3 Phonons
413(7)
14.3.1 Goldstone Counting Revisited
413(2)
14.3.2 Effective Action
415(3)
14.3.3 Perfect Fluids
418(2)
14.4 Summary
420(3)
Exercises
421(2)
15 Degenerate Systems
423(38)
15.1 Fermi Liquids
426(10)
15.1.1 EFT Near a Fermi Surface
426(2)
15.1.2 Irrelevance of Fermion Self-Interactions
428(5)
15.1.3 Marginal Interactions
433(3)
15.2 Superconductivity and Fermion Pairing
436(9)
15.2.1 Phonon Scaling
436(5)
15.2.2 Phonon-Coulomb Competition
441(4)
15.3 Quantum Hall Systems
445(12)
15.3.1 Hall and Ohmic Conductivity
445(3)
15.3.2 Integer Quantum Hall Systems
448(4)
15.3.3 Fractional Quantum Hall Systems
452(5)
15.4 Summary
457(4)
Exercises
458(3)
16 EFTs and Open Systems
461(53)
16.1 Thermal Fluids
462(5)
16.1.1 Statistical Framework
463(2)
16.1.2 Evolution through Conservation
465(2)
16.2 Open Systems
467(5)
16.2.1 Density Matrices
468(2)
16.2.2 Reduced Time Evolution
470(2)
16.3 Mean Fields and Fluctuations
472(23)
16.3.1 The Mean/Fluctuation Split
473(3)
16.3.2 Neutrinos in Matter
476(5)
16.3.3 Photons: Mean-Field Evolution
481(8)
16.3.4 Photons: Scattering and Fluctuations
489(5)
16.3.5 Domain of Validity of Mean-Field Theory
494(1)
16.4 Late Times and Perturbation Theory
495(12)
16.4.1 Late-Time Resummation
496(4)
16.4.2 Master Equations
500(7)
16.5 Summary
507(7)
Exercises
508(6)
Appendix A Conventions and Units 514(15)
Appendix B Momentum Eigenstates and Scattering 529(10)
Appendix C Quantum Field Theory: A Cartoon 539(38)
Appendix D Further Reading 577(14)
References 591(45)
Index 636
C. P. Burgess is a professor at both McMaster University and the Perimeter Institute for Theoretical Physics, and co-author of the book The Standard Model: A Modern Primer. He is a Fellow of the Royal Society of Canada and has been awarded the CAP/CRM medal for Theoretical Physics. After initially learning about effective field theories from his PhD supervisor, Nobel Laureate Steven Weinberg, he is now a world expert on their applications throughout physics.