量子场论

Preface for students

Preface for instructors

Acknowledgments

Part I Spin Zero

1 Attempts at relativistic quantum mechanics

2 Lorentz invariance (prerequisite： 1)

3 Canonical quantization of scalar fields (2)

4 The spin-statistics theorem (3)

5 The LSZ reduction formula (3)

6 Path integrals in quantum mechanics

7 The path integral for the harmonic oscillator (6)

8 The path integral for free field theory (3， 7)

9 The path integral for interacting field theory (8)

10 Scattering amplitudes and the Feynman rules (5， 9)

11 Cross sections and decay rates (10)

12 Dimensional analysis with h = c = i (3)

13 The Lehmann-Kallen form of the exact propagator (9)

14 Loop corrections to the propagator (10， 12， 13)

15 The one-loop correction in Lehmann-Kallen form (14)

16 Loop corrections to the vertex (14)

17 Other 1PI vertices (16)

18 Higher-order corrections and renormalizability (17)

19 Perturbation theory to all orders (18)

20 Two-particle elastic scattering at one loop (19)

21 The quantum action (19)

22 Continuous symmetries and conserved currents (8)

23 Discrete symmetries： P， T， C， and Z (22)

24 Nonabelian symmetries (22)

25 Unstable particles and resonances (14)

26 Infrared divergences (20)

27 Other renormalization schemes (26)

28 The renormalization group (27)

29 Effective field theory (28)

30 Spontaneous symmetry breaking (21)

31 Broken symmetry and loop corrections (30)

32 Spontaneous breaking of continuous symmetries (22， 30)

Part II Spin One Half

33 Representations of the Lorentz group (2)

34 Left- and right-handed spinor fields (3， 33)

35 Manipulating spinor indices (34)

36 Lagrangians for spinor fields (22， 35)

37 Canonical quantization of spinor fields I (36)

38 Spinor technology (37)

39 Canonical quantization of spinor fields II (38)

40 Parity， time reversal， and charge conjugation (23， 39)

41 LSZ reduction for spin-one-half particles (5， 39)

42 The free fermion propagator (39)

43 The path integral for fermion fields (9， 42)

44 Formal development of fermionic path integrals (43)

45 The Feynman rules for Dirac fields (10， 12， 41， 43)

46 Spin sums (45)

47 Gamma matrix technology (36)

48 Spin-averaged cross sections (46， 47)

49 The Feynman rules for Majorana fields (45)

50 Massless particles and spinor helicity (48)

51 Loop corrections in Yukawa theory (19， 40， 48)

52 Beta functions in Yukawa theory (28， 51)

53 Functional determinants (44， 45)

Part III Spin One

54 Maxwells equations (3)

55 Electrodynamics in Coulomb gauge (54)

56 LSZ reduction for photons (5， 55)

57 The path integral for photons (8， 56)

58 Spinor electrodynamics (45， 57)

59 Scattering in spinor electrodynamics (48， 58)

60 Spinor helicity for spinor electrodynamics (50， 59)

61 Scalar electrodynamics (58)

62 Loop corrections in spinor electrodynamics (51， 59)

63 The vertex function in spinor electrodyna， mics (62)

64 The magnetic moment of the electron (63)

65 Loop corrections in scalar electrodynamics (61， 62)

66 Beta functions in quantum electrodynamics (52， 62)

67 Ward identities in quantum electrodynamics I (22， 59)

68 Ward identities in quantum electrodynamics II (63， 67)

69 Nonabelian gauge theory (24， 58)

70 Group representations (69)

71 The path integral for nonabelian gauge theory (53， 69)

72 The Feynman rules for nonabelian gauge theory (71)

73 The beta function in nonabelian gauge theory (70， 72)

74 BRST symmetry (70， 71)

75 Chiral gauge theories and anomalies (70， 72)

76 Anomalies in global symmetries (75)

77 Anomalies and the path integral for fermions (76)

78 Background field gauge (73)

79 Gervais-Neveu gauge (78)

80 The Feynman rules for N x N matrix fields (10)

81 Scattering in quantum chromodynamics (60， 79， 80)

82 Wilson loops， lattice theory， and confinement (29， 73)

83 Chiral symmetry breaking (76， 82)

84 Spontaneous breaking of gauge symmetries (32， 70)

85 Spontaneously broken abelian gauge theory (61， 84)

86 Spontaneously broken nonabelian gauge theory (85)

87 The Standard Model： gauge and Higgs sector (84)

88 The Standard Model： lepton sector (75， 87)

89 The Standard Model： quark sector (88)

90 Electroweak interactions of hadrons (83， 89)

91 Neutrino masses (89)

92 Solitons and monopoles (84)

93 Instantons and theta vacua (92)

94 Quarks and theta vacua (77， 83， 93)

95 Supersymmetry (69)

96 The Minimal Supersymmetric Standard Model (89， 95)

97 Grand unification (89)

Bibliography

Index

I have tried to make the subject as accessible to beginners as possible. There are three main aspects to my approach. Logical development of the basic concepts. This is， of course， very different from the historical development of quantum field theory， which， like the historical development of most worthwhile subjects， was filled with inspired guesses and brilliant extrapolations of sometimes fuzzy ideas， as well as its fair share of mistakes， misconceptions， and dead ends. None of that is in this book. From this book， you will (I hope) get the impression that the whole subject is effortlessly clear and obvious， with one step following the next like sunshine after refreshing rain.