1st Edition

A Course in Field Theory

By Pierre van Baal Copyright 2014
    234 Pages 28 B/W Illustrations
    by CRC Press

    Extensively classroom-tested, A Course in Field Theory provides material for an introductory course for advanced undergraduate and graduate students in physics. Based on the author’s course that he has been teaching for more than 20 years, the text presents complete and detailed coverage of the core ideas and theories in quantum field theory. It is ideal for particle physics courses as well as a supplementary text for courses on the Standard Model and applied quantum physics.

    The text gives students working knowledge and an understanding of the theory of particles and fields, with a description of the Standard Model toward the end. It explains how Feynman rules are derived from first principles, an essential ingredient of any field theory course. With the path integral approach, this is feasible. Nevertheless, it is equally essential that students learn how to use these rules. This is why the problems form an integral part of this book, providing students with the hands-on experience they need to become proficient.

    Taking a concise, practical approach, the book covers core topics in an accessible manner. The author focuses on the basics, offering a balanced mix of topics and rigor for intermediate physics students.

    Quantisation of Fields
    Euler–Lagrange Equations
    Tree-Level Diagrams
    Hamiltonian Perturbation Theory
    Path Integrals in Quantum Mechanics
    Path Integrals in Field Theory
    Perturbative Expansion in Field Theory
    The Scattering Matrix
    Cross Sections
    Decay Rates
    The Dirac Equation
    Plane Wave Solutions of the Dirac Equation
    The Dirac Hamiltonian
    Path Integrals for Fermions
    Feynman Rules for Vector Fields
    Quantum Electrodynamics—QED
    Non-Abelian Gauge Theories
    The Higgs Mechanism
    Gauge Fixing and Ghosts
    The Standard Model
    Loop Corrections and Renormalisation


    Pierre van Baal

    "… a pleasant novelty that manages the impossible: a full course in field theory from a derivation of the Dirac equation to the standard electroweak theory in less than 200 pages. Moreover, the final chapter consists of a careful selection of assorted problems, which are original and either anticipate or detail some of the topics discussed in the bulk of the chapters. Instead of building a treatise out of a collection of lecture notes, the author took the complementary approach and constructed a course out of a number of well-known and classic treatises. The result is fresh and useful. … the mathematical approach is rigorous, and readers are never spoon-fed but encouraged to focus on the few essential themes of each lecture. … This book will be useful not only for masters-level students but will, I hope, be well received by teachers and practitioners in the field."
    CERN Courier, May 2014