Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Viet Dang Nguyen (Lyon I)
I will present an overview of results obtained with Bin Zhang (Sichuan University). We will start by giving a simple example which shows the necessity to subtract infinities in quantum field theory. Then we introduce the notion of Feynman amplitudes and study their singularities using a zeta regularization with several parameters. Finally we will apply this method to perturbative renormalization of quantum field theories on Riemannian manifolds.