Quantum field theories without infinities and naturalness

The standard way to do computations in Quantum Field Theory (QFT) is plagued by infinities and fine-tunings leading to the conception of "naturalness", which requires the cancellation of quadratic divergences by new particles with masses right above the Fermi scale. At the same time, the ultimate outcome of any QFT (the Standard Model in particular) is the prediction of all kinds of finite particle cross-sections in terms of a few finite input parameters (such as the mass of an electron and fine-structure constant in quantum electrodynamics). In this talk, I will describe how to relate the parameters of the theory to observables without running into divergences in Feynman diagrams. The existence of such a technique suggests that the "hierarchy problem" is not really physical, but rather an artifact of the conventional procedure of renormalisation of QFTs.