Olga Aryasova (Inst. of Geophysics, Nat. Acad. of Sciences of Ukraine / Friedrich–Schiller–Univ. Jena)
Estanislao Herscovich (UJF Grenoble)
R. Borcherds has introduced a different point of view to formalise perturbative Quantum Field Theory (pQFT), which shares however several features with other well-known constructions in the literature (see the work by E. Stueckelberg and A. Petermann, by H. Epstein and V. Glaser, and, more recently, by R. Brunetti, K. Fredenhagen and their collaborators, and by C. Brouder, B. Fauser, A. Frabetti, R. Oeckl, to mention a few). In this talk I will summarise the basic ingredients in the construction of a pQFT (à la Borcherds), and I will sketch the main constructions in the involved steps, as well as the fundamental results. I will also discuss some of the gaps in the exposition of Borcherds and how they should/could be filled. This is ongoing work, the first part of which can be found in my manuscript "Renormalization in Quantum Field Theory", available at https://www-fourier.ujf-grenoble.fr/~eherscov.