Quantum elecrodynamics near material boundaries

Quantum electrodynamics in free-space is a well-understood and a very successful theory. This is not the case when polarizable boundaries are present, which is a common scenario. The presence of reflective surfaces affects the photon field. Thereby the quantummechanical vacuum fluctuations of the electromagnetic field are constrained leading to changes in the interaction energies of charged particles which are directly measurable. One of the most famous examples of such an effect is the Lamb shift of an atom in front of a perfectly reflecting mirror, which depends on the distance of the atom from the mirror, thus giving rise to an attractive force - the so-called Casimir-Polder force. This thesis touches upon current challenges of quantum electrodynamics with externally applied boundary conditions, which is of increasing importance for nanotechnology and its applications in physics, chemistry and biology. When studying the abovementioned vacuum effects one can use models of various degrees of sophistication for the material properties that need to be taken into account. The simplest is to assume perfect reflectivity. This leads to simple boundary conditions on the electromagnetic field and thereby its quantum fluctuations. The difficulty of such calculations then lies only in the possibly complex geometry of the macroscopic body. The next possible level of sophistication is to allow imperfect reflectivity. The simplest way to achieve this is by considering a material with constant and frequency-independent refractive index. However, for all real material surfaces the reflectivity is frequency-dependent. Causality then requires that dispersion is accompanied by absorption. The aim of this project was twofold: (i) to construct, using well-understood tools of theoretical physics, the microscopic theory of quantum systems, like atoms, interacting with macroscopic polarizable media, which would facilitate relatively simple perturbative calculations of QED corrections due to the presence of boundaries, (ii) to apply the developed formalism to the calculation of the Casimir-Polder force between an atom and a realistic material.