Electrodynamics of correlated electron systems

Physical and chemical systems can be characterized by their natural frequency and energy scales. It is hardly an exaggeration that most of what we know about such systems, from the acoustics of a violin to the energy levels of atoms, comes from their response to perturbations at these natural frequencies. It is of course the same situation in `correlated' electron materials. We can learn about the novel effects of strong electron-electron interactions and the properties of collective states of matter (superconductors, quantum magnets etc.) by characterizing their response to small amplitude perturbations at their natural frequencies. In solids, these natural frequency scales span an impressively large frequency range from x-ray down to DC. This incredibly broad range means that a blizzard of experimental techniques and analysis methods are required for the characterization of correlated systems with optical techniques. This short review and lecture notes attempt to lay out a brief summary of the formalism, techniques, and analysis used for `optical' spectroscopies of correlated electron systems. They are idiosyncratic, occasionally opinionated, and - considering the breadth of the subject - incredibly brief.