Quantisation of the Electromagnetic Field and Spontaneous Photon Emission

We develop the method of canonical quantisation for the case of the free electromagnetic field. We choose the Coulomb gauge, which has a simpler physical interpretation. We introduce the creation and annihilation operators in this framework. The formalism is applied to the problem of spontaneous emission of radiation from an excited atomic state at first order in the perturbation expansion. This allows us to obtain a concrete physical result, namely the computation of an excited state decay rate, and, at the same time, have a first look at abstract concepts, such as gauge invariance and renormalisation.

QED Response of the Vacuum

We present a new perspective of the link between QED and Maxwell's equations. We demonstrate that the interpretation of $\mathbf{D}=\varepsilon_{0} \mathbf{E}$ as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter, runs as it should.

Optical Helicity and Chirality: Conservation and Sources

We consider the helicity and chirality of the free electromagnetic field, and advocate the former as a means of characterising the interaction of chiral light with matter. This is in view of the intuitive quantum form of the helicity density operator, and of the dual symmetry transformation generated by its conservation. We go on to review the form of the helicity density and its associated continuity equation in free space, in the presence of local currents and charges, and upon interaction with bulk media, leading to characterisation of both microscopic and macroscopic sources of helicity.