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.