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Scalar BMS-invariant QFT defined on the causal boundary $\scri$ of anasymptotically flat spacetime is discussed. (a)(i) It is noticed that thenatural $BMS$ invariant pure quasifree state $\lambda$ on $\cW(\scri)$,recently introduced by Dappiaggi, Moretti an Pinamonti, enjoys positivity ofthe self-adjoint generator of $u$-translations with respect to {\em every}Bondi coordinate frame $(u,\z,\bz)$ on $\scri$, $u\in \bR$ being the affineparameter of the null geodesics forming $\scri$. This fact may be interpretedas a remnant of spectral condition inherited from Minkowski spacetime. (ii) Itis proved cluster property under $u$-displacements holds for $u$-invariant purestate on $\cW(\scri)$. (iii) It is proved that there is a unique algebraic purequasifree state invariant under $u$-displacements (of a fixed Bondi frame)having positive self-adjoint generator of $u$-displacements. It coincides withthe GNS-invariant state $\lambda$.(iv) It is showed that in the folium of apure $u$-invariant state $\omega$ (not necessarily quasifree) on $\cW(\scri)$,$\omega$ is the only state invariant under $u$-displacement. (b) It is provedthat the theory can formulated for spacetimes asymptotically flat at nullinfinity which admit future time completion. In this case a $*$-isomorphism$\imath$ exists which identifies the (Weyl) algebra of observables of linearfields in the bulk with a sub algebra of $\cW(\scri)$. A preferred state on thefield algebra in the bulk is induced by the $BMS$-invariant state $\lambda$.Comment: Final version, accepted for publication in Commun. Math. Phy

communications in mathematical physics/communications in mathematical physics

Uniqueness Theorem for BMS-Invariant States of Scalar QFT on the Null Boundary of Asymptotically Flat Spacetimes and Bulk-Boundary Observable Algebra Correspondence