紹介
Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results to thorough treatments of modern topics such as the renormalization group, spinor-helicity methods for quark and gluon scattering, magnetic monopoles, instantons, supersymmetry, and the unification of forces. The book is written in a modular format, with each chapter as self-contained as possible, and with the necessary prerequisite material clearly identified. It is based on a year-long course given by the author and contains extensive problems, with password protected solutions available to lecturers at www.cambridge.org/9780521864497.
目次
Preface for students
Preface for instructors
Acknowledgements
Part I. Spin Zero: 1. Attempts at relativistic quantum mechanics
2. Lorentz invariance
3. Canonical quantization of scalar fields
4. The spin-statistics theorem
5. The LSZ reduction formula
6. Path integrals in quantum mechanics
7. The path integral for the harmonic oscillator
8. The path integral for free field theory
9. The path integral for interacting field theory
10. Scattering amplitudes and the Feynman rules
11. Cross sections and decay rates
12. Dimensional analysis with ?=c=1
13. The Lehmann-Kallen form
14. Loop corrections to the propagator
15. The one-loop correction in Lehmann-Kallen form
16. Loop corrections to the vertex
17. Other 1PI vertices
18. Higher-order corrections and renormalizability
19. Perturbation theory to all orders
20. Two-particle elastic scattering at one loop
21. The quantum action
22. Continuous symmetries and conserved currents
23. Discrete symmetries: P, T, C, and Z
24. Nonabelian symmetries
25. Unstable particles and resonances
26. Infrared divergences
27. Other renormalization schemes
28. The renormalization group
29. Effective field theory
30. Spontaneous symmetry breaking
31. Broken symmetry and loop corrections
32. Spontaneous breaking of continuous symmetries
Part II. Spin One Half: 33. Representations of the Lorentz Group
34. Left- and right-handed spinor fields
35. Manipulating spinor indices
36. Lagrangians for spinor fields
37. Canonical quantization of spinor fields I
38. Spinor technology
39. Canonical quantization of spinor fields II
40. Parity, time reversal, and charge conjugation
41. LSZ reduction for spin-one-half particles
42. The free fermion propagator
43. The path integral for fermion fields
44. Formal development of fermionic path integrals
45. The Feynman rules for Dirac fields
46. Spin sums
47. Gamma matrix technology
48. Spin-averaged cross sections
49. The Feynman rules for majorana fields
50. Massless particles and spinor helicity
51. Loop corrections in Yukawa theory
52. Beta functions in Yukawa theory
53. Functional determinants
Part III. Spin One: 54. Maxwell's equations
55. Electrodynamics in coulomb gauge
56. LSZ reduction for photons
57. The path integral for photons
58. Spinor electrodynamics
59. Scattering in spinor electrodynamics
60. Spinor helicity for spinor electrodynamics
61. Scalar electrodynamics
62. Loop corrections in spinor electrodynamics
63. The vertex function in spinor electrodynamics
64. The magnetic moment of the electron
65. Loop corrections in scalar electrodynamics
66. Beta functions in quantum electrodynamics
67. Ward identities in quantum electrodynamics I
68. Ward identities in quantum electrodynamics II
69. Nonabelian gauge theory
70. Group representations
71. The path integral for nonabelian gauge theory
72. The Feynman rules for nonabelian gauge theory
73. The beta function for nonabelian gauge theory
74. BRST symmetry
75. Chiral gauge theories and anomalies
76. Anomalies in global symmetries
77. Anomalies and the path integral for fermions
78. Background field gauge
79. Gervais-Neveu gauge
80. The Feynman rules for N x N matrix fields
81. Scattering in quantum chromodynamics
82. Wilson loops, lattice theory, and confinement
83. Chiral symmetry breaking
84. Spontaneous breaking of gauge symmetries
85. Spontaneously broken abelian gauge theory
86. Spontaneously broken nonabelian gauge theory
87. The standard model: Gauge and Higgs sector
88. The standard model: Lepton sector
89. The standard model: Quark sector
90. Electroweak interactions of hadrons
91. Neutrino masses
92. Solitons and monopoles
93. Instantons and theta vacua
94. Quarks and theta vacua
95. Supersymmetry
96. The minimal supersymmetric standard model
97. Grand unification
Bibliography.
