4th Edition

# Gauge Theories in Particle Physics: A Practical Introduction, Volume 1 From Relativistic Quantum Mechanics to QED, Fourth Edition

**Also available as eBook on:**

**Volume 1** of this revised and updated edition provides an accessible and practical introduction to the first gauge theory included in the Standard Model of particle physics: quantum electrodynamics (QED).

The book includes self-contained presentations of electromagnetism as a gauge theory as well as relativistic quantum mechanics. It provides a unique elementary introduction to quantum field theory, establishing the essentials of the formal and conceptual framework upon which the subsequent development of the three gauge theories is based. The text also describes tree-level calculations of physical processes in QED and introduces ideas of renormalization in the context of one-loop radiative corrections for QED.

**New to the Fourth Edition**

- New chapter on Lorentz transformations and discrete symmetries in relativistic quantum mechanics, with physical applications
- Introduction of Majorana fermions at an early stage, making the material suitable for a first course in relativistic quantum mechanics
- Discrete symmetries in quantum field theory
- Updates on nucleon structure functions and the status of QED

The authors discuss the main conceptual points of the theory, detail many practical calculations of physical quantities from first principles, and compare these quantitative predictions with experimental results, helping readers improve both their calculation skills and physical insight.

INTRODUCTORY SURVEY, ELECTROMAGNETISM AS A GAUGE THEORY, AND RELATIVISTIC QUANTUM MECHANICS

The Particles and Forces of in the Standard Model

Electromagnetism as a Gauge Theory

Relativistic Quantum Mechanics

Lorentz Transformations and Discrete Symmetries

INTRODUCTION TO QUANTUM FIELD THEORY

Quantum Field Theory I: The Free Scalar Field

Quantum Field Theory II: Interacting Scalar Fields

Quantum Field Theory III: Complex Scalar Fields, Dirac and Maxwell Fields; Introduction of Electromagnetic Interactions

TREE-LEVEL APPLICATIONS IN QED

Elementary Processes in Scalar and Spinor Electrodynamics

Deep Inelastic Electron-Nucleon Scattering and the Parton Model

LOOPS AND RENORMALIZATION

Loops and Renormalization I: The ABC Theory

Loops and Renormalization II: QED

APPENDIX A: Non-Relativistic Quantum Mechanics

APPENDIX B: Natural Units

APPENDIX C: Maxwell's Equations: Choice of Units

APPENDIX D: Special Relativity: Invariance and Covariance

APPENDIX E: Dirac Delta-Function

APPENDIX F: Contour Integration

APPENDIX G: Green Functions

APPENDIX H: Elements of Non-Relativistic Scattering Theory

APPENDIX I: The Schrödinger and Heisenberg Pictures

APPENDIX J: Dirac Algebra and Trace Identities

APPENDIX K: Example of a Cross Section Calculation

APPENDIX L: Feynman Rules for Tree Graphs in QED

References

Index

*Problems appear at the end of each chapter.*

### Biography

**Ian J.R. Aitchison** is Emeritus Professor of Physics at the University of Oxford and a visiting scientist at SLAC National Accelerator Laboratory. He has previously held research positions at Brookhaven National Laboratory, Saclay, and the University of Cambridge. He was a visiting professor at the University of Rochester and the University of Washington, and a scientific associate at CERN. Dr. Aitchison has published over 90 scientific papers mainly on hadronic physics and quantum field theory. He is the author of *Relativistic Quantum Mechanics*, *An Informal Introduction to Gauge Field Theories*, and *Supersymmetry in Particle Physics* and joint editor of two other books.

**Anthony J.G. Hey** is Vice President of Microsoft Research Connections, where he is responsible for the worldwide external research and technical computing strategy across Microsoft Corporation. A fellow of the U.K. Royal Academy of Engineering, Dr. Hey was previously the director of the U.K. e-Science Initiative and the head of the School of Electronics and Computer Science and dean of Engineering and Applied Science at the University of Southampton. His research interests encompass parallel programming for parallel systems built from mainstream commodity components. With Jack Dongarra, Rolf Hempel, and David Walker, he wrote the first draft of a specification for a new message-passing standard called MPI. This initiated the process that led to the successful MPI standard of today.

"Aitchison and Hey was the ‘bible’ for me as a young post-doc in the 1980s … The book has been revised regularly as the field progressed and I am delighted to see a new edition which brings it up to date to the discovery of a Higgs-like boson at the LHC in July 2012. As an experimentalist, this book helped me understand the theoretical underpinnings of my work. Its strength has always been the combination of the theory with discussion of experimental results. The new edition continues this tradition by including background on discrete symmetries … This will become a new classic."

—Amanda Cooper-Sarkar, Oxford University, UK"This is an indispensable textbook for all particle physicists, experimentalists and theorists alike, providing an accessible exposé of the Standard Model, covering the mathematics used to describe it and some of the most important experimental results which vindicate it. As a lecturer in an advanced course on the Standard Model for experimentalists, I use the books for the more theoretical aspects and as a constant source for clear explanations of the underlying physics. I also know it to be the recommended text on numerous theoretical modules in particle physics. … these textbooks will remain on the top of a high energy physicist’s reading list for years to come."

—Matthew Wing, University College London, UK