Diagrammatica : the path to Feynman rules / Martinus Veltman.

Format:

Book

Author/Creator:

Veltman, Martinus.

Series:

Cambridge lecture notes in physics ; 4.

Cambridge lecture notes in physics ; 4

Language:

English

Subjects (All):

Quantum field theory.

Feynman diagrams.

Physical Description:

xii, 284 pages ; 23 cm.

Place of Publication:

Cambridge : Cambridge University Press, 1994.

Summary:

This book provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. The aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules, and to outline their domain of applicability. The book begins with a brief review of some aspects of Einstein's theory of relativity that are of particular importance for field theory, before going on to consider the relativistic quantum mechanics of free particles, interacting fields, and particles with spin. The techniques learnt in the chapters are then demonstrated in examples that might be encountered in real accelerator physics. Further chapters contain discussions on renormalization, massive and massless vector fields and unitarity. A final chapter presents concluding arguments concerning quantum electrodynamics. The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. An appendix containing a comprehensive summary of the rules and conventions used is followed by an appendix specifying the full Lagrangian of the Standard Model and the corresponding Feynman rules. To make the book useful for a wide audience, a final appendix provides a discussion on the metric used, and an easy-to-use dictionary connecting equations written with a different metric. Written as a textbook, many diagrams and examples are included.

This book will be used by beginning graduate students taking courses in particle physics or quantum field theory, as well as by researchers as a source and reference book on Feynman diagrams and rules.

Contents:

1 Lorentz and Poincare Invariance 1

1.1 Lorentz Invariance 1

1.2 Structure of the Lorentz Group 7

1.3 Poincare Invariance 10

1.4 Maxwell Equations 10

1.5 Notations and Conventions 12

2 Relativistic Quantum Mechanics of Free Particles 15

2.1 Hilbert Space 15

2.2 Matrices in Hilbert Space 22

2.3 Fields 25

2.4 Structure of Hilbert Space 29

3 Interacting Fields 32

3.1 Physical System 32

3.2 Hilbert Space 33

3.3 Magnitude of Hilbert Space 34

3.4 U-matrix, S-matrix 35

3.5 Interpolating Fields 39

3.6 Feynman Rules 46

3.7 Feynman Propagator 54

3.8 Scattering Cross Section 55

3.9 Lifetime 60

3.10 Numerical Evaluation 62

3.11 Schrodinger Equation, Bound States 62

4 Particles with Spin 68

4.1 Representations of the Lorentz Group 68

4.2 The Dirac Equation 76

4.3 Fermion Fields 79

4.4 The E.M. Field 85

4.5 Quantum Electrodynamics 87

4.6 Charged Vector Boson Fields 91

4.7 Electron-Proton Scattering. The Rutherford Formula 92

5 Explorations 98

5.1 Scattering Cross Section for e[superscript +]e[superscript -] [right arrow] [mu superscript + mu superscript -] 98

5.2 Pion Decay. Two Body Phase Space. Cabibbo Angle 101

5.3 Vector Boson Decay 105

5.4 Muon Decay. Fiertz Transformation 108

5.5 Hyperon Leptonic Decay 117

5.6 Pion Decay and PCAC 124

5.7 Neutral Pion Decay and PCAC 131

6 Renormalization 137

6.2 Loop Integrals 137

6.3 Self Energy 145

6.4 Power Counting 148

6.5 Quantum Electrodynamics 151

6.6 Renormalizable Theories 153

6.7 Radiative Corrections: Lamb Shift 154

6.8 Radiative Corrections: Top Correction to [rho]-Parameter 157

6.9 Neutral Pion Decay and the Anomaly 162

7 Massive and Massless Vector Fields 169

7.1 Subsidiary Condition Massive Vector Fields 169

7.2 Subsidiary Condition Massless Vector Fields 171

7.3 Photon Helicities 173

7.4 Propagator and Polarization Vectors of Massive Vector Particles 174

7.5 Photon Propagator 177

7.6 Left Handed Photons 180

8 Unitarity 183

8.1 U-matrix 183

8.2 Largest Time Equation 185

8.3 Cutting Equations 187

8.4 Unitarity and Cutting Equation 191

8.5 Unitarity: General Case 197

8.6 Kallen-Lehmann Representation, Dispersion Relation 200

8.7 Momenta in Propagators 204

9 Quantum Electrodynamics: Finally 207

9.1 Unitarity 207

9.2 Ward Identities 208

Appendix A Complex Spaces, Matrices, CBH Equation 213

A.2 Differentiation of Matrices 217

A.3 Functions of Matrices 218

A.4 The CBH Equation 220

Appendix B Traces 224

B.2 Multi-Dimensional [gamma]-Matrices 230

B.3 Frequently Used Equations 231

Appendix C Dimensional Regularization 233

Appendix D Summary: Combinatorial Factors 243

D.2 External Lines, Spin Sums, Propagators 245

D.3 Combinatorial Factors 247

Appendix E Standard Model 249

E.1 Lagrangian 249

E.2 Feynman Rules 258

Appendix F Metric and Conventions 273

F.2 Translation Examples 279

F.3 Translation Dictionary 281.

Notes:

Includes index.

ISBN:

0521456924

OCLC:

30778684