Some recent results in linear scalar quantum field the - ory in globally hyperbolic asymptotically flat space - times

The content of this paper is that of an invited plenary talk at the XVII SIGRAV Conference held in Torino, September 4-7, 2006. Some recent results obtained by the author and collaborators about QFT in asymptotically flat spacetimes at null infinity are reviewed. In particular it is shown that bosonic QFT can be defined on the null boundary I of any asymptotically flat spacetime M . This theory admits a state λ 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 λ induces in the bulk spacetime M a state, λM , 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 λM enjoys the global Hadamard property so that it is suitable for locally covariant perturbative renormalization procedures. 1 Asymptotically Flat Spacetimes and BMS group Asymptotically flat spacetimes – by definition – have a certain asymptotic structure. The main motivation of the works in the references [1, 2, 3] has been investigating if that asymptotic structure determines canonically preferred states in every asymptotically flat spacetime for (linear) scalar quantum field theory. The properties of those states have been also focused. Let us remind the main definition [4] (See [5] for further discussions and references). Definition 1. (Asymptotically flat vacuum spacetime at future null infinity) A four dimensional spacetime (M, g) is called asymptotically flat vacuum spacetime at future null infinity if: (a) (M, g) can be seen as an embedded submanifold of a larger spacetime (M̃, g̃) with g̃↾M= Ω g, Ω being a smooth function on M̃ , strictly positive on M . (b) I := ∂M , called future null infinity of M , is a 3-dim M̃ -submanifold satisfying (i) Ω↾I+= 0 but dΩ↾I+ 6= 0,