By Joel Franklin
Cambridge University Press
This book provides a comprehensive introduction to classic field theory, which concerns the generation and interaction of fields and is the logical precursor of quantum field theory. But, while in most university physics programmes students are taught classical mechanics first and then quantum mechanics, quantum field theory is normally not preceded by dedicated classic field theory classes. The author, though, claims that it would be worth giving more room to classical field theory, since it can offer a good way to think about modern physical model building.
The focus is on the relativistic structural elements of field theories, which enable a deeper understanding of Maxwell’s equations and of the electromagnetic field theory. The same also stands for other areas of physics, such as gravity.
The book comprises four chapters and is completed by three appendices. The first chapter provides a review of special relativity, with some in-depth discussion of transformations and invariants. Chapter two focuses on Green’s functions and their role as integral building blocks, offering as examples static problems in electricity and the full wave equation of electromagnetism. In chapter three, Lagrangian mechanics is introduced, together with the notions of a field Lagrangian and of action. The last chapter is dedicated to gravity, another classic field theory. The appendices include mathematical and numerical methods useful for field theories and a short essay on how one can take a compact action and from it develop all the physics known from EM.
Written for advanced-undergraduate and graduate students, this book is meant for dedicated courses on classical field theory, but could also be used in combination with other texts for advanced classes on EM or a course on quantum field theory. It could also be used as a reference text for self-study.
