Claudio Dappiaggi

On the role of asymptotic structures in QFT on curved backgrounds


The aim of these lectures is to advocate that asymptotic structures play a pivotal role in the analysis of quantum field theory over curved backgrounds. Particularly, we shall thoroughly discuss the example of asymptotically flat spacetimes and we will focus our attention on the geometric structure of the so-called conformal boundary. This turns out to be a three dimensional null differentiable manifold on which it is possible to encode the information of a suitable scalar field theory living in the bulk of the chosen asymptotically flat spacetime. This realization of the so-called ``holographic principle'' will be discussed both at a classical and at a quantum level; in the latter case it will be most notably exploited as a tool to uncover a distinguished algebraic state of Hadamard form for the quantum bulk field theory.