# Quantum Field Theory

Cambridge University Press, 1/25/2007

EAN 9780521864497, ISBN10: 0521864496

Hardcover, 660 pages, 24.7 x 17.4 x 3.7 cm

Language: English

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.

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-KÃƒÂ¤llÃƒÂ©n form

14. Loop corrections to the propagator

15. The one-loop correction in Lehmann-KÃƒÂ¤llÃƒÂ©n 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.

'This accessible and conceptually structured introduction to quantum field theory will be of value not only to beginning students but also to practicing physicists interested in learning or reviewing specific topics. The book is organized in a modular fashion, which makes it easy to extract the basic information relevant to the reader's area(s) of interest. The material is presented in an intuitively clear and informal style. Foundational topics such as path integrals and Lorentz representations are included early in the exposition, as appropriate for a modern course; later material includes a detailed description of the Standard Model and other advanced topics such as instantons, supersymmetry, and unification, which are essential knowledge for working particle physicists, but which are not treated in most other field theory texts.' Washington Taylor, Massachusetts Institute of Technology