Claudio Dappiaggi - Quantum field theory on asymptotically flat spacetimes and the BMS group

This talk was part of the Thematic Programme on "Carrollian Physics and Holography" held at the ESI April 2 -- 26, 2024.
We review the cornerstones of a longstanding programme aimed at constructing Hadamard states for free quantum fields on four-dimensional asymptotically flat spacetimes by exploiting invariance under the action of the BMS asymptotic symmetry group. In particular we outline how this procedure has been used to give a rigorous construction of the Unruh state for a massless, conformally coupled, real scalar field on Schwarzschild spacetime and we survey its application to higher spin, free fields. To conclude we examine the future perspectives of this approach and we comment in particular on the existing obstructions to deal with interacting models.