This is a book on classical field theory, with a focus on the most studied one: electricity and magnetism (E&M). It was developed to fill a gap in the current undergraduate physics curriculum – most departments teach classical mechanics and then quantum mechanics, the idea being that one informs the other and logically precedes it. The same is true for the pair “classical field theory” and “quantum field theory,” except that there are almost no dedicated classical field theory classes. Instead, the subject is reviewed briefly at the start of a quantum field theory course. There are a variety of reasons why this is so, most notably because quantum field theory is enormously successful and, as a language, can be used to describe three of the four forces of nature. The only classical field theory (of the four forces of nature) that requires the machinery developed in this book is general relativity, which is not typically taught at the undergraduate level. Other applications include fluid mechanics (also generally absent from the undergraduate course catalogue) and “continuum mechanics” applications, but these tend to be meant primarily for engineers.

Yet classical field theory provides a good way to think about modern physical model building, in a time where such models are relevant. In this book, we take the “bottom up” view of physics, that there are certain rules for constructing physical theories. Knowing what those rules are and what happens to a physical model when you break or modify them is important in developing physical models beyond the ones that currently exist. One of the main points of the book is that if you ask for a “natural” vector field theory, one that is linear (so superposition holds) and is already “relativistic,” you get Maxwell's E&M almost uniquely. This idea is echoed in other areas of physics, notably in gravity, where if you similarly start with a second rank symmetric field that is linear and relativistic, and further require the universal coupling that is the hallmark of gravity, you get general relativity (almost uniquely).