This book provides an accessible introduction to quantum electrodynamics. Based on lectures on quantum electrodynamics given by the highly original and distinguished physicist V. N. Gribov, the aim of the book is to present the theory of quantum electrodynamics in the shortest and clearest way for applied use. A distinctive feature of Gribov's approach is the systematic use of the Green function method which allows a straightforward generalization to the cases of strong and weak interactions. The book starts with an introduction that uses the basics of quantum mechanics to gently introduce the reader into the world of propagation functions and particle interactions. The following chapter then focusses on spin 1/2 particles. The text goes on to discuss symmetries, the CPT theorem, causality, and unitarity followed by a detailed presentation of renormalisation theory. A final chapter looks at difficulties with the theory and possible routes to their resolution.

Foreword

xi

Particles and their interactions in relativistic quantum mechanics

1

(84)

The propagator

1

(4)

The Green function

5

(8)

The Green function for a system of particles

7

(1)

The momentum representation

8

(4)

Virtual particles

12

(1)

The scattering amplitude

13

(4)

How to calculate physical observables

13

(3)

Poles in the scattering amplitude and the bound states

16

(1)

The electromagnetic field

17

(8)

Photons in an `external field'

25

(11)

Relativistic propagator

25

(2)

Relativistic interaction

27

(3)

Relativistic Green function

30

(3)

Propagation of vector photons

33

(3)

Free massive relativistic particles

36

(2)

Interactions of spinless particles

38

(8)

Interaction of spinless particles with the electromagnetic field

46

(5)

Examples of the simplest electromagnetic processes

51

(5)

Scattering of charged particles

52

(2)

The Compton effect (photon-π-meson scattering)

54

(2)

Diagrams and amplitudes in momentum representation

56

(3)

Photon emission amplitude in momentum space

56

(1)

Meson-meson scattering via photon exchange

57

(1)

Feynman rules

58

(1)

Amplitudes of physical processes

59

(16)

The unitarity condition

61

(1)

S-matrix

61

(4)

Invariant scattering amplitude

65

(1)

Cross section

65

(2)

2 → 2 scattering

67

(1)

π-π- scattering

68

(3)

π+π- scattering

71

(4)

The Mandelstam plane

75

(5)

The Compton effect (for π-mesons)

80

(5)

Particles with spin 1/2. Basic quantum electrodynamic processes

85

(59)

Free particles with spin 1/2

85

(13)

The Green function of the electron

98

(2)

Matrix elements of electron scattering amplitudes

100

(2)

Electron-photon interaction

102

(3)

Electron-electron scattering

105

(7)

Connection between spin and statistics

106

(5)

Electron charge

111

(1)

The Compton effect

112

(13)

Compton scattering at small energies

121

(2)

Compton scattering at high energies

123

(2)

Electron-positron annihilation into two photons

125

(5)

Annihilation near threshold

128

(1)

e+e- annihilation at very high energies

128

(2)

Electron scattering in an external field

130

(2)

Electron bremsstrahlung in an external field

132

(5)

Emission of a soft photon by a low energy electron

133

(2)

Soft radiation off a high energy electron

135

(2)

The Weizsacker-Williams formula

137

(7)

General properties of the scattering amplitude

144

(30)

Symmetries in quantum electrodynamics

144

(9)

P-conservation

144

(3)

T-invariance

147

(3)

C-invariance

150

(3)

The CPT theorem

153

(3)

PT-invariant amplitudes

155

(1)

Causality and unitarity

156

(18)

Causality

156

(4)

Analytic properties of the Born amplitudes

160

(2)

Scattering amplitude as an analytic function

162

(2)

Unitarity

164

(3)

Born amplitudes and unitarity

167

(3)

How to restore perturbation theory on the basis of unitarity and analyticity, or perturbation theory without Feynman graphs

170

(4)

Radiative corrections. Renormalization

174

(67)

Higher order corrections to the electron and photon Green functions

174

(8)

Multiloop contributions to the electron Green function

174

(5)

Multiloop contributions to the photon Green function

179

(3)

Renormalization of the electron mass and wave function

182

(5)

Renormalization of the photon Green function

187

(5)

Feynman rules for multiloop scattering amplitudes

192

(1)

Renormalization of the vertex part

193

(6)

The generalized Ward identity

199

(3)

Radiative corrections to electron scattering in an external field

202

(19)

One-loop polarization operator

204

(9)

One-loop vertex part

213

(8)

The Dirac equation in an external field

221

(13)

Electron in the field of a supercharged nucleus

230

(4)

Radiative corrections to the energy levels of hydrogen-like atoms. The Lamb shift

234

(7)

Difficulties of quantum electrodynamics

241

(26)

Renormalization and divergences

241

(17)

Divergences of Feynman diagrams

242

(7)

Renormalization

249

(9)

The zero charge problem in quantum electrodynamics

258

(9)

References

267

(1)

Index

268

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