Astérisque, n° 412. Renormalization in quantum field theory (after R. Borcherds)

The aim of this manuscript is to provide a complete and precise formulation of the renormalization picture for perturbative Quantum Field Theory (pQFT) on general curved spacetimes introduced by Borcherds in [R. E. Borcherds, « Renormalization and quantum field theory, » Algebra Number Theory 5 (2011) 627-658]. More precisely, we give a full proof of the free and transitive action of the group of renormalizations on the set of Feynman measures associated with a local precut propagator, and that such a set is nonempty if the propagator is further assumed to be manageable and of cut type. Even though we follow the general principles laid by Borcherds in loc. cit., we have in many cases proceeded differently to prove his claims, and we have also needed to add some hypotheses to be able to prove the corresponding statements.