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E-raamat: Problems in Quantum Field Theory: With Fully-Worked Solutions

(Commissariat à l'Energie Atomique (CEA), Saclay)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 26-Aug-2021
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108985901
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Problems in Quantum Field Theory: With Fully-Worked SolutionsSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 26-Aug-2021
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9781108985901
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This collection of problems in Quantum Field Theory, accompanied by their complete solutions, aims to bridge the gap between learning the foundational principles and applying them practically. The carefully chosen problems cover a wide range of topics, starting from the foundations of Quantum Field Theory and the traditional methods in perturbation theory, such as LSZ reduction formulas, Feynman diagrams and renormalization. Separate chapters are devoted to functional methods (bosonic and fermionic path integrals; worldline formalism), to non-Abelian gauge theories (Yang-Mills theory, Quantum Chromodynamics), to the novel techniques for calculating scattering amplitudes and to quantum field theory at finite temperature (including its formulation on the lattice, and extensions to systems out of equilibrium). The problems range from those dealing with QFT formalism itself to problems addressing specific questions of phenomenological relevance, and they span a broad range in difficulty, for graduate students taking their first or second course in QFT.

This collection of problems in Quantum Field Theory, accompanied by their complete solutions, bridges the gap between learning the foundational principles and applying them practically. The carefully chosen problems cover a wide range of topics and difficulty levels, suitable for graduate students taking their first or second course in QFT.

Arvustused

' a valuable bridge between textbook treatments and the modern literature and is an example of the type of volume often reported to be missing from the shelves. Libraries that serve universities teaching quantum field theory, or any institution with active research programs involving quantum field theory, should acquire this book ... Recommended.' M. C. Ogilvie, Choice Connect

Muu info

A collection of problems in QFT, with complete solutions, for graduate students taking their first or second course.
List of Figures and Tables
x
Preface xii
Acknowledgements xiv
Notation and Conventions xv
1 Quantum Field Theory Basics
1(70)
Introduction
1(10)
1 Relationship between the Equations of Motion of Φ and Φin
11(1)
2 Little-Group Elements for Massless Particles
12(3)
3 S-matrix in Terms of Φin and Φout
15(2)
4 Constraints on the S-matrix from Causality
17(5)
5 Landau Equations for Soft and Collinear Singularities
22(6)
6 Multi-loop Integration in D Dimensions
28(3)
7 Weinberg Convergence Theorem
31(3)
8 Electron Anomalous Magnetic Moment
34(4)
9 Ward-Takahashi Identities and Lorentz Invariance
38(3)
10 Equivalence Principle and Lorentz Invariance
41(1)
11 Lee-Nauenberg Theorem
42(7)
12 Classical External Field Approximation
49(4)
13 Subleading Soft Radiation in Scalar QED
53(4)
14 Low-Burnett-Kroll Theorem
57(5)
15 Coherent States in Quantum Field Theory
62(2)
16 Running Couplings in a Two-Field Scalar Field Theory
64(4)
17 Solution of the Running Equation at Two Loops
68(3)
2 Functional Methods
71(59)
Introduction
71(6)
18 Weyl Quantization
77(2)
19 Combinatorial Interpretation of the Legendre Transform
79(4)
20 Coherent State Path Integral
83(3)
21 Coherent State Path Integral (Continued)
86(4)
22 Spin Coherent States and the Berry Phase
90(11)
23 Zeta Function Regularization of the Klein-Gordon Operator
101(2)
24 Casimir Zero-Point Energy
103(3)
25 The Feynman Diagrams behind the Casimir Force
106(4)
26 Gross-Neveu Model
110(4)
27 D'Hoker-Gagne Formula
114(4)
28 Stochastic Quantization
118(5)
29 Complex Langevin Equation
123(7)
3 Non-Abelian Fields
130(75)
Introduction
130(7)
30 Basic su(η) Identities
137(1)
31 More su(η) Identities
138(2)
32 More su(η) Identities (Continued)
140(2)
33 Ansu(2) Identity
142(2)
34 Area Derivative of a Wilson Loop
144(1)
35 Endpoint Derivative of a Wilson Line
145(3)
36 Makeenko-Migdal Loop Equation
148(3)
37 Classical Non-Abelian Particles and the Wong Equations
151(3)
38 Wong Equations from the Worldline Formalism
154(3)
39 Non-Abelian Stokes's Theorem
157(5)
40 QED in the't Hooft-Veltman Gauge
162(5)
41 LSZ Reduction Formula and Gauge Invariance
167(4)
42 Large-N Expansion in SU(N) Yang-Mills Theory
171(4)
43 Soft Radiation and Antenna Effects in QCD
175(8)
44 An Identity Obeyed by On-Shell QCD Amplitudes
183(1)
45 Low-Burnetr-Kroll Theorem in QCD
184(4)
46 Globally Gauge Invariant Operators
188(3)
47 Banks-Zaks Fixed Points
191(2)
48 Instantons and Tunneling in Quantum Mechanics
193(3)
49 Instantons as Transitions between Pure Gauges in Yang-Mills Theory
196(3)
50 Vacua of Yang-Mills Theory
199(6)
4 Scattering Amplitudes
205(71)
Introduction
205(7)
51 Enumeration of Tree Graphs
212(2)
52 Six-Point---+ + + Amplitude
214(2)
53 Two Spinor-Helicity Identities
216(2)
54 Auxiliary Vector Dependence of the Polarization Vectors
218(2)
55 Polarization Sum in the Spinor-Helicity Formalism
220(1)
56 Photon Decoupling Identity
221(2)
57 Scalar-Antiscalar-Gluon Amplitudes
223(3)
58 Color Decomposition with a Quark-Antiquark Pair
226(3)
59 Quark-Antiquark-Gluon Amplitudes
229(4)
60 Quark-Antiquark-Gluon Amplitudes (Continued)
233(5)
61 Gluon-Gluon Scattering in the Spinor-Helicity Framework
238(4)
62 Soft Limit of Gluon Amplitudes
242(5)
63 Collinear Limit of Gluon Amplitudes
247(5)
64 Enumeration of One-Loop Graphs
252(6)
65 Ultraviolet Finiteness of One-Loop All-Plus Amplitudes
258(1)
66 Rationality of One-Loop All-Plus Amplitudes
259(2)
67 One-Loop Four-Point + + + + Amplitude from Generalized Unitarity
261(6)
68 One-Loop Five-Point + + + + + Amplitude from Generalized Unitarity
267(9)
5 Lattice, Finite T, Strong Fields
276(77)
Introduction
276(7)
69 Banks-Casher Relation
283(2)
70 Nielsen-Ninomiya Theorem
285(5)
71 Wigner Transform of a Convolution Product
290(3)
72 Center Symmetry and Deconfinement
293(4)
73 Photon Hard Thermal Loop from Classical Particles
297(4)
74 Gluon Hard Thermal Loop from Colored Classical Particles
301(4)
75 Landau-Pomeranchuk-Migdal Effect
305(7)
76 Microcanonical Equilibration in φ4 Scalar Theory
312(3)
77 Combinatorics of Multi-particle Production
315(5)
78 Generating Functional for Particle Production
320(4)
79 Correlations in the Schwinger Mechanism
324(7)
80 Schwinger Mechanism from Bogoliubov Transformations
331(8)
81 Unruh Effect, Hawking Radiation
339(8)
82 Anderson Localization
347(3)
83 Scaling Theory of Anderson Localization
350(3)
Index 353
François Gelis is a researcher at the Institut de Physique Théorique of CEA-Saclay, France. He received his M.S. from École Normale Supérieure de Lyon and a Ph.D. from the Université de Savoie. His research area is the theoretical study of the extreme phases of matter produced in heavy ion collisions. This led him to develop new Quantum Field Theory techniques to handle the strong fields encountered in these situations, for which he was awarded the Paul Langevin prize of the French physical society in 2015. He has taught QFT at École Polytechnique since 2016.
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