Perturbative renormalization by flow equations of boundary field theory

In this talk, we give an overview of the proof of perturbative renormalization of a (massive) scalar field theory with a quartic self-interaction on the four dimensional Euclidean half-space. For a particular choice of the renormalization conditions, we explain how the effective action associated to the Robin and Neumann boundary conditions can be expressed as the sum of the effective action corresponding to the translationally invariant theory, plus a remainder which consists of surface counter-terms that renormalize the Robin parameter. In the case of Dirichlet boundary conditions, no surface counter-terms are required to render the theory finite.