Gauge Field Notes

Textbook

Peskin & SchroederSchwarzSrednicki
01

Attempts at relativistic quantum mechanics

02

Lorentz Invariance (prerequisite 1)

03

Canonical Quantization of Scalar Fields (2)

04

The Spin-Statistics Theorem (3)

05

The LSZ Reduction Formula (3)

06

Path Integrals in Quantum Mechanics

07

The Path Integral for the Harmonic Oscillator (6)

08

The Path Integral for Free Field Theory (3, 7)

09

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 $ hbar = c = 1$ (3)

13

The Lehmann-Källén Form of the Exact Propagator (9)

14

Loop Corrections to the Propagator (10, 12, 13)

15

The One-Loop Correction in Lehmann-Källén Form (14)

16

Loop Corrections to the Vertex (14)

17

Other 1PI Vertices (16)

18

Higher-Order Corrections and Renormalizability (17)

20

Two-Particle Elastic Scattering at One Loop (19)

21

The Quantum Action (19)

22

Continuous Symmetries and Conserved Currents (8)

24

Nonabelian Symmetries (22)

27

Other Renormalization Schemes (26)

28

The Renormalization Group (27)

29

Effective Field Theory (28)

32

Spontaneous Breaking of Continuous Symmetries (22, 30)

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)

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)

45

The Feynman Rules for Dirac Fields (10, 12, 41, 43)

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)

55

Electrodynamics in Coulomb Gauge (54)

56

LSZ Reduction for Photons (5, 55)

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 Electrodynamics (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)

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)

80

The Feynman Rules for $N times N$ 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)

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)

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)