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Preface v
QED and QCD 1
One-loop diagrams 3
Divergences, regularization and renormalization 3
Massive vacuum diagram 6
Integrals in d dimensions 9
Feynman parametrization 13
Massless propagator diagram 14
Tensors and [gamma]-matrices in d dimensions 17
QED at one loop 21
Lagrangian and Feynman rules 21
Photon propagator 23
Ward identity 25
Photon self-energy 27
Photon field renormalization 28
Electron propagator 30
Vertex and charge renormalization 33
Electron mass 39
QCD at one loop 43
Lagrangian and Feynman rules 43
Quark propagator 48
Gluon propagator 49
Ghost propagator 52
Quark-gluon vertex 53
Coupling constant renormalization 54
Ghost-gluon vertex 56
Three-gluon vertex 58
Four-gluon vertex 65
Two-loop corrections in QED and QCD 73
Massless propagator diagram 73
Photon self-energy 79
Photon field renormalization 82
Charge renormalization 87
Electron self-energy 89
Electron field renormalization 93
Two-loop corrections in QCD 97
On-shell renormalization scheme 101
On-shell renormalization of photon field 101
One-loop massive on-shell propagator diagram 103
On-shell renormalization of electron mass and field 106
On-shell charge 109
Magnetic moment 111
Two-loop massive vacuum diagram 116
On-shell renormalization of photon field and charge at two loops 118
On-shell renormalization in QCD 119
Decoupling of heavy-particle loops 121
Photon field 121
Electron field 124
Charge 127
Electron mass 129
Decoupling in QCD 131
Conclusion: Effective field theories 135
Colour factors 141
Bibliography 155
Multiloop calculations 157
Massless propagator diagrams 159
Introduction 159
One loop 160
Two loops 162
Three loops 168
G(1, 1, 1, 1, n) 171
Non-planar basis integral 175
HQET propagator diagrams 179
Crash course of HQET 179
One loop 181
Two loops 182
Three loops 187
J(1, 1, n, 1, 1) 189
I(1, 1, 1, 1, n) 191
Massive on-shell propagator diagrams 197
One loop 197
Two loops 199
Two loops, two masses 202
Three loops 205
Hypergeometric functions and multiple [Zeta] values 209
Multiple [Zeta] values 209
Expanding hypergeometric functions in [epsilon]: an example 215
Expanding hypergeometric functions in [epsilon]: the algorithm 218
Bibliography 221
Index 223
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