Uniqueness theorem for BMS-invariant states of scalar QFT on the null boundary of asymptotically flat spacetimes and bulk-boundary observable algebra correspondence
type: Item
instance of: scholarly article
title: Uniqueness theorem for BMS-invariant states of scalar QFT on the null boundary of asymptotically flat spacetimes and bulk-boundary observable algebra correspondence
zbMATH Open document ID: 1141.81028
author: Valter Moretti
published in: Communications in Mathematical Physics
publication date: 2007-09-11T00:00:00Z
full work available at URL: https://arxiv.org/abs/gr-qc/0512049
review text: The paper originates from results previously reported by the same author and his collaborators in Ref. [\textit{C. Dappiaggi, V. Moretti} and \textit{N. Pinamonti}, Rev. Math. Phys. 18, No. 4, 349--415 (2006; Zbl 1107.81040)], thus aiming at providing a better understanding of features of scalar QFT defined on the causal boundary \({\mathfrak I}^+\) of an asymptotically flat at null infinity spacetime and based on a certain Weyl algebra \(\mathcal{W} ({\mathfrak I}^+)\) of observables associated to a symplectic space invariant under the action of the Bondi-Metzner-Sachs (BMS) group. The author basically addresses two questions. The first one concerns peculiarities of BMS-invariant states. In this respect the author shows that that: 1) the natural BMS-invariant state on \(\mathcal{W} ({\mathfrak I}^+)\) (the Gelfand-Naimark-Segal invariant state also considered in [Dappiaggi, Moretti and N. Pinamonti (loc. cit.)]) enjoys positivity of the self-adjoint generator of the affine parameter displacements w.r.t. every admissible frame (i.e. w.r.t. every global frame on the boundary \({\mathfrak I}^+\) related with a Bondi frame on \({\mathfrak I}^+\) by means of a BMS transformation); 2) the validity of positivity for the self-adjoint generator of affine parameter translations in a fixed admissible frame individuates such state uniquely; 3) in the folium of a pure state on \(\mathcal{W} ({\mathfrak I}^+)\) which is invariant under affine parameter displacement, the state itself is the only state possessing the invariance. The author next moves to the second issue, which regards the possibility to isometrically map the Weyl algebra of linear QFT in the bulk onto a sub-algebra of the BMS-invariant Weyl algebra \(\mathcal{W} ({\mathfrak I}^+)\) and, consequently, to induce a preferred state in the bulk by the natural BMS-invariant state. He proves, in fact, that the required isometric \(\ast\)-homomorphism do exist for the class of space-times that are flat at null infinity an…
reviewed by: G. Landolfi
Mathematics Subject Classification ID: 81T20
Mathematics Subject Classification ID: 46L60
Mathematics Subject Classification ID: 46N50
Mathematics Subject Classification ID: 81R15
Mathematics Subject Classification ID: 83C30
Mathematics Subject Classification ID: 81S10
zbMATH DE Number: 5189602
zbMATH Keywords: asymptotically flat spacetimes
zbMATH Keywords: BMS group
zbMATH Keywords: algebraic quantum field theory
zbMATH Keywords: Weyl algebra
MaRDI profile type: Publication
OpenAlex ID: W2018427849
arXiv ID: gr-qc/0512049
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DOI: 10.1007/S00220-006-0107-0
description: scientific article