Problems in quantum field theory : with fully-worked solutions / François Gelis.

Format:

Book

Author/Creator:

Gelis, François, 1972- author.

Language:

English

Subjects (All):

Quantum field theory.

Physical Description:

1 online resource (xiii, 357 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2021.

Summary:

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.

Contents:

Cover

Half-title

Title page

Copyright information

Dedication

Epigraph

Contents

List of Figures and Tables

Preface

Acknowledgements

Notation and Conventions

1 Quantum Field Theory Basics

Introduction

1. Relationship between the Equations of Motion of [phi] and [phi[sub(in)]

2. Little-Group Elements for Massless Particles

3. S-matrix in Terms of [phi[sub(in)] and [phi[sub(out)]

4. Constraints on the S-matrix from Causality

5. Landau Equations for Soft and Collinear Singularities

6. Multi-loop Integration in D Dimensions

7. Weinberg Convergence Theorem

8. Electron Anomalous Magnetic Moment

9. Ward-Takahashi Identities and Lorentz Invariance

10. Equivalence Principle and Lorentz Invariance

11. Lee-Nauenberg Theorem

12. Classical External Field Approximation

13. Subleading Soft Radiation in Scalar QED

14. Low-Burnett-Kroll Theorem

15. Coherent States in Quantum Field Theory

16. Running Couplings in a Two-Field Scalar Field Theory

17. Solution of the Running Equation at Two Loops

2 Functional Methods

18. Weyl Quantization

19. Combinatorial Interpretation of the Legendre Transform

20. Coherent State Path Integral

21. Coherent State Path Integral (Continued)

22. Spin Coherent States and the Berry Phase

23. Zeta Function Regularization of the Klein-Gordon Operator

24. Casimir Zero-Point Energy

25. The Feynman Diagrams behind the Casimir Force

26. Gross-Neveu Model

27. D'Hoker-Gagn[acute(e)] Formula

28. Stochastic Quantization

29. Complex Langevin Equation

3 Non-Abelian Fields

30. Basic su(n) Identities

31. More su(n) Identities

32. More su(n) Identities (Continued)

33. An su(2) Identity

34. Area Derivative of a Wilson Loop

35. Endpoint Derivative of a Wilson Line.

36. Makeenko-Migdal Loop Equation

37. Classical Non-Abelian Particles and the Wong Equations

38. Wong Equations from the Worldline Formalism

39. Non-Abelian Stokes's Theorem

40. QED in the 't Hooft-Veltman Gauge

41. LSZ Reduction Formula and Gauge Invariance

42. Large-N Expansion in SU(N) Yang-Mills Theory

43. Soft Radiation and Antenna Effects in QCD

44. An Identity Obeyed by On-Shell QCD Amplitudes

45. Low-Burnett-Kroll Theorem in QCD

46. Globally Gauge Invariant Operators

47. Banks-Zaks Fixed Points

48. Instantons and Tunneling in Quantum Mechanics

49. Instantons as Transitions between Pure Gauges in Yang-Mills Theory

50. Vacua of Yang-Mills Theory

4 Scattering Amplitudes

51. Enumeration of Tree Graphs

52. Six-Point −−−+++ Amplitude

53. Two Spinor-Helicity Identities

54. Auxiliary Vector Dependence of the Polarization Vectors

55. Polarization Sum in the Spinor-Helicity Formalism

56. Photon Decoupling Identity

57. Scalar-Antiscalar-Gluon Amplitudes

58. Color Decomposition with a Quark-Antiquark Pair

59. Quark-Antiquark-Gluon Amplitudes

60. Quark-Antiquark-Gluon Amplitudes (Continued)

61. Gluon-Gluon Scattering in the Spinor-Helicity Framework

62. Soft Limit of Gluon Amplitudes

63. Collinear Limit of Gluon Amplitudes

64. Enumeration of One-Loop Graphs

65. Ultraviolet Finiteness of One-Loop All-Plus Amplitudes

66. Rationality of One-Loop All-Plus Amplitudes

67. One-Loop Four-Point ++++ Amplitude from Generalized Unitarity

68. One-Loop Five-Point +++++ Amplitude from Generalized Unitarity

5 Lattice, Finite T, Strong Fields

69. Banks-Casher Relation

70. Nielsen-Ninomiya Theorem

71. Wigner Transform of a Convolution Product

72. Center Symmetry and Deconfinement.

73. Photon Hard Thermal Loop from Classical Particles

74. Gluon Hard Thermal Loop from Colored Classical Particles

75. Landau-Pomeranchuk-Migdal Effect

76. Microcanonical Equilibration in [phi[sup(4)] Scalar Theory

77. Combinatorics of Multi-particle Production

78. Generating Functional for Particle Production

79. Correlations in the Schwinger Mechanism

80. Schwinger Mechanism from Bogoliubov Transformations

81. Unruh Effect, Hawking Radiation

82. Anderson Localization

83. Scaling Theory of Anderson Localization

Index.

Notes:

Title from publisher's bibliographic system (viewed on 20 Aug 2021).

ISBN:

1-108-98590-4

1-108-97668-9

OCLC:

1276857071