Exact Results in Quantum Theory & Gravity

In this talk I will present the framework of perturbative algebraic quantum field theory (pAQFT), developed over theyears by Brunetti, Duetsch, Fredenhagen, myself and many others. This approach allows one to mathematically describephysically relevant QFT models in Lorentzian signature (also on curved spacetimes). It combines the locality idea coming from algebraic quantum field theory (AQFT) with methods of perturbation theory, including homological algebra and formal deformation quantisation. Recently a non-perturbative version of the framework has been started by Buchholz and Fredenhagen and is currently under development by Brunetti, Duetsch, Fredenhagen and myself.