Quantum Field Theory

Synopsis

Quantum field theory (QFT), the language of particle physics, is crucial to a physicist's graduate education. Based on lecture notes for courses taught for many years at Radboud University in the Netherlands, this book presents an alternative approach to teaching QFT using Feynman diagrams. A diagrammatic approach to understanding QFT exposes young physicists to an orthogonal introduction to the theory, bringing new ways to understand challenges in the field. Diagrammatic techniques using Feynman diagrams are used didactically, starting from simple discussions in lower dimensions to more complex topics in the Standard Model. Worked examples and exercises, for which solutions are available online, help the reader develop a deep understanding and intuition that enhances their problem-solving skills and understanding of QFT. Classroom-tested, this accessible book is valuable resource for graduate students and researchers.

Summary

Chapter 1: Introduction

* Introduction to the fundamental concepts of quantum field theory (QFT), including fields, particles, and the Lagrangian.
* Example: The Lagrangian for the electromagnetic field describes the behavior of photons, quanta of light.

Chapter 2: Classical Fields

* Derivation of the Euler-Lagrange equations of motion from the Lagrangian.
* Example: The Maxwell equations for the electromagnetic field are derived from its Lagrangian.

Chapter 3: Quantization of Fields

* Introduction to the quantization of classical fields.
* Example: The quantization of the electromagnetic field leads to the existence of photons, obeying Bose-Einstein statistics.

Chapter 4: Feynman Diagrams and Scattering Processes

* Introduction to Feynman diagrams, which represent interactions between particles.
* Example: The Feynman diagram for electron-electron scattering depicts the exchange of a photon.

Chapter 5: Quantum Electrodynamics (QED)

* Detailed treatment of QED, the theory of the electromagnetic interaction between charged particles.
* Example: The QED prediction of the anomalous magnetic moment of the electron has been experimentally verified to high precision.

Chapter 6: The Strong Nuclear Force

* Introduction to quantum chromodynamics (QCD), the theory of the strong nuclear force.
* Example: The confinement property of QCD explains why quarks are only observed in bound states (hadrons).

Chapter 7: The Weak Nuclear Force

* Introduction to the electroweak theory, which unifies the weak and electromagnetic forces.
* Example: The Higgs mechanism gives mass to the W and Z bosons, mediators of the weak force.

Chapter 8: Quantum Field Theory in Curved Spacetime

* Extension of QFT to include gravity.
* Example: The interaction of a scalar field with the gravitational field is described by the Klein-Gordon equation in curved spacetime.

Chapter 9: Effective Field Theories

* Introduction to effective field theories, which describe phenomena at energies below a cut-off scale.
* Example: The Fermi theory of beta decay is an effective field theory describing the weak decay of neutrons.

Chapter 10: Beyond the Standard Model

* Discussion of extensions to the Standard Model, including supersymmetry, dark matter, and extra dimensions.
* Example: Supersymmetry postulates the existence of superpartners for all known particles, such as the squark and the photino.