The Feynman Propagator on Perturbations of Minkowski Space

Gell-Redman, Jesse; Haber, Nick; Vasy, András

doi:10.1007/s00220-015-2520-8

Cited by 34 publications

(52 citation statements)

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“…It is worth mentioning that this formalism has been succesfully applied to General Relativity and plays an important rôle in the recently announced resolution of the Kerr-de Sitter stability conjecture by Hintz and Vasy [HV16]. It was also recently applied to Quantum Field Theory (on asymptotically Minkowski spacetimes) [GHV16,Va16,VW15], though in the present work it is used in a different way.…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes

Wrochna

2017

Lett Math Phys

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In the setting of asymptotically Anti-de Sitter spacetimes, we consider Klein-Gordon fields subject to Dirichlet boundary conditions, with mass satisfying the Breitenlohner-Freedman bound. We introduce a condition on the b-wave front set of two-point functions of quantum fields, which locally in the bulk amounts to the usual Hadamard condition, and which moreover allows to estimate wave front sets for the holographically induced theory on the boundary. We prove the existence of two-point functions satisfying this condition, and show their uniqueness modulo terms that have smooth Schwartz kernel in the bulk and have smooth restriction to the boundary. Finally, using Vasy's propagation of singularities theorem, we prove an analogue of Duistermaat & Hörmander's theorem on distinguished parametrices.2010 Mathematics Subject Classification. 81T13, 81T20, 35S05, 35S35.

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Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

The holographic Hadamard condition on asymptotically anti-de Sitter spacetimes

Wrochna

2017

Lett Math Phys

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“…With the (non-standard, see Footnote 1) conventions used in the present paper, the operators P −1 {±} , denoted also P −1 ± , are precisely the advanced/retarded propagators. On the other hand, the remaining two, P −1 ∅ and P −1 {+,−} , are named Feynman and anti-Feynman propagator [29] and we show that they have indeed the same wave front set as the Feynman/anti-Feynman parametrices of Duistermaat and Hörmander [19].…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 66%

“…We will use in particular the following result from [64], cf. also the discussion in [29]. (1) If m < 1 2 − l and m is nonincreasing along the bicharacteristic flow in the direction approaching R i , then…”

Section: B-regularity and Propagation Of Singularitiesmentioning

confidence: 91%

“…retarded propagator defined in the usual way as in the introduction (modulo smoothing terms if P −1 I is just a parametrix). The name Feynman propagator for P −1 ∅ can be justified by relating it to a Feynman parametrix in the sense of Duistermaat and Hörmander [19], as pointed out in [29,63] (and analogously for the anti-Feynman one). Here we make this precise by proving that the Schwartz kernel of P −1 ∅ (considered as a distribution on M • × M • ) has wave front set of precisely the same form as the Feynman parametrix' of Duistermaat and Hörmander, and therefore the two operators coincide modulo smoothing terms (at least provided (M • , g) is globally hyperbolic so that the assumptions in [19] are satisfied).…”

Section: Propagatorsmentioning

confidence: 99%

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Quantum Fields from Global Propagators on Asymptotically Minkowski and Extended de Sitter Spacetimes

Vasy

Wrochna

2018

Ann. Henri Poincaré

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We consider the wave equation on asymptotically Minkowski spacetimes and the Klein-Gordon equation on even asymptotically de Sitter spaces. In both cases we show that the extreme difference of propagators (i.e. retarded propagator minus advanced, or Feynman minus anti-Feynman), defined as Fredholm inverses, induces a symplectic form on the space of solutions with wave front set confined to the radial sets. Furthermore, we construct isomorphisms between the solution spaces and symplectic spaces of asymptotic data. As an application of this result we obtain distinguished Hadamard two-point functions from asymptotic data. Ultimately, we prove that non-interacting Quantum Field Theory on asymptotically de Sitter spacetimes extends across the future and past conformal boundary, i.e. to a region represented by two even asymptotically hyperbolic spaces. Specifically, we show this to be true both at the level of symplectic spaces of solutions and at the level of Hadamard two-point functions. P Λ ± = Λ ± P = 0, Λ + − Λ − = i(P −1 + − P −1 − ), Λ ± ≥ 0,

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“…I´d ata have only one component. This can be thought of as the analogue of the fact that on Minkowski space, the Feynman inverse discussed in [21] or [19,20,12] coincides with the well-familiar Feynman propagator canonically associated with the vacuum state.…”

Section: 2mentioning

confidence: 97%