The talk will address the existence of a perturbation expansion for the partition function of the properly renormalised Phi-four measure on the three-dimensional torus. This existence is a well-known result from constructive field theory, but we will argue that using Wiener chaos expansion and modern algebraic techniques based on Hopf algebras, the proof can be substantially simplified. We will also briefly comment on the (more difficult) issue of Borel summability of the perturbation expansion. This is joint work with Tom Klose (Berlin), see https://arxiv.org/abs/2207.08555
