In this paper, we provide a simple pedagogical proof of the existence of covariant renormalizations in Euclidean perturbative quantum field theory on closed Riemannian manifolds, following the Epstein–Glaser philosophy. We rely on a local method that allows us to extend a distribution defined on an open set [Formula: see text] to the whole manifold [Formula: see text].
We express the first non-vanishing Massey–Milnor linkings in terms of Chern–Simons–Witten configuration space integrals in perturbative quantum field theory.
Perturbative Quantum Field Theory on Random Trees
