Electromagnetism

Abstract

Since the interactions treated in this book all are of electromagnetic origin this chapter on electromagnetism takes a central part of the background material. We start, in Sect. 2.1 by discussing Maxwell’s equations; we give these on differential form and also on Fourier transformed form. Then we motivate our choice of unit system, in Sect. 2.2. Next, in Sect. 2.3, we treat the constitutive relations relating the auxiliary fields, D and H, to the true fields, E and B ; here we also discuss the different versions of the auxiliary fields depending on the book keeping of the sources. In derivations, it is often easier to handle potentials instead of the fields themselves. This motivates the section, Sect. 2.4, on potentials in which we also discuss gauge transformations and in particular the Coulomb and Lorentz gauges. A very important factor for the formation of the normal modes of the system is how the fields behave at the boundary between regions. This is governed by the boundary conditions, Sect. 2.5. These, result in the Fresnel equations, Sect. 2.6. We have added a section, Sect. 2.7, on how to handle 2D sheets in the system. Finally, we end with the fields from time-dependent electric and magnetic dipoles, in Sect. 2.8; these are needed in the derivation of the Casimir-Polder interactions between atoms.