Understanding the Electromagnetic Field

Understanding the Electromagnetic Field is an entry level textbook for graduate students with a focus on the electromagnetic field. This book explores the relationship between the field and electric charges.

The earlier part of the book deals with the derivation of Maxwell's equations from experimental laws. Next, the electromagnetic field is studied in the light of special relativity, leading logically to the quantum theory of radiation. Quantum mechanics is introduced as a quantum field theory of the electromagnetic field. The rules of quantum mechanics are developed in a systematic way, with relativistic quantum electrodynamics explaining some puzzles that emerge in classical electrodynamics. A chapter is devoted to the study of angular momentum in quantum mechanics, uniquely showing its importance in the understanding of the interaction between the field and charges. The geometry of the space in which the electromagnetic field is embedded is shown to be significant. General relativity provides a relationship between the geometry of space and the presence of matter. The final chapter is devoted to deriving the fundamental equations of general relativity. Mathematical expressions are derived for the effect of gravity on the electromagnetic field, and measurable results are calculated.

The prerequisites of this book are Newtonian physics, calculus and linear algebra. Exercises are provided throughout the book.