Lectures On Qed And Qcd: Practical Calculation And Renormalization Of One- And Multi-loop Feynman Diagrams

by Andrey Grozin

Overview

The increasing precision of experimental data in many areas of elementary particle physics requires an equally precise theoretical description. In particular, radiative corrections (described by one- and multi-loop Feynman diagrams) have to be considered. Although a growing number of physicists are involved in such projects, multi-loop calculation methods can only be studied from original publications. With its coverage of multi-loop calculations, this book serves as an excellent supplement to the standard textbooks on quantum field theory. Based around postgraduate-level lectures given by the author, the material is suitable for both beginners and graduate students.

Product Details

ISBN-13:	9789812569141
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	01/24/2007
Pages:	236
Product dimensions:	6.20(w) x 9.10(h) x 1.10(d)

Table of Contents

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