Some recent results in linear scalar quantum field theory in globally hyperbolic asymptotically flat spacetimes

This work concerns some recent results obtained by the author and collaborators about QFT in asymptotically flat spacetimes at infinity. In particular it is shown that bosonic QFT can be defined on the boundary =+ of any asymptotically flat spacetime M. This theory admits a state which is uniquely determined from invariance under BMS group and a BMS-energy positivity requirement. There is a nice interplay with bosonic (massless, conformally coupled) QFT defined in the bulk spacetime. In particular, under suitable further requirements, the universal state induces in the bulk spacetime M a state, M, which enjoys the following remarkable properties. It reduces to standard Minkowski vacuum whenever M is Minkowski spacetime and in the general case, it is invariant under the group of isometries of the spacetime M, it is a ground state (i.e. it satisfies the positive energy condition) with respect to any timelike Killing time of M without zero-modes, finally M enjoys the global Hadamard property so that it is suitable for locally covariant perturbative renormalization procedures. (The content of this paper is that of an invited plenary talk at the XVII SIGRAV Conference held in Torino, September 4-7, 2006)