On the Reeh-Schlieder Property in Curved Spacetime

Sanders, Ko

doi:10.1007/s00220-009-0734-3

Cited by 39 publications

(75 citation statements)

References 25 publications

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“…The main problem is that the Fulling-Narcowich-Wald deformation argument [FNW] used to prove Thm. 2.6 does not apply anymore as the interpolating metric g is not real analytic (though at least a weaker form of the Reeh-Schlieder property can be obtained, and an abstract existence argument can be given for states satisfying the full Reeh-Schlieder property, see [Sa1]).…”

Section: Existence Of Analytic Hadamard States On Analytic Spacetimesmentioning

confidence: 99%

Analytic Hadamard States, Calderón Projectors and Wick Rotation Near Analytic Cauchy Surfaces

Gérard

Wrochna

2019

Commun. Math. Phys.

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We consider the Klein-Gordon equation on analytic spacetimes with an analytic Cauchy surface. In this setting, we prove the existence of pure analytic Hadamard states. The proof is based on considering an elliptic operator obtained by Wick rotating the Klein-Gordon operator in a neighborhood of a Cauchy hypersurface. The Cauchy data of Hadamard two-point functions are constructed as Calderón projectors (suitably generalized if the hypersurface is non-compact) for the elliptic operator.2010 Mathematics Subject Classification. 81T13, 81T20, 35S05, 35S35.

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Section: Existence Of Analytic Hadamard States On Analytic Spacetimesmentioning

confidence: 99%

Analytic Hadamard States, Calderón Projectors and Wick Rotation Near Analytic Cauchy Surfaces

Gérard

Wrochna

2019

Commun. Math. Phys.

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“…From an axiomatic quantum field theory perspective, this seems very closely connected to the Reeh-Schlieder theorem [20]. Even though it has not been proven in curved space, there is a strong believe that such a theorem should exist [21](see also [22]).…”

Section: Resultsmentioning

confidence: 99%

Comments on a state-operator correspondence for the torus

Belin

Kruthoff

2018

SciPost Phys.

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We investigate the existence of a state-operator correspondence on the torus. This correspondence would relate states of the CFT Hilbert space living on a spatial torus to the path integral over compact Euclidean manifolds with operator insertions. Unlike the states on the sphere that are associated to local operators, we argue that those on the torus would more naturally be associated to line operators. We find evidence that such a correspondence cannot exist and in particular, we argue that no compact Euclidean path integral can produce the vacuum on the torus. Our arguments come solely from field theory and formulate a CFT version of the Horowitz-Myers conjecture for the AdS soliton.

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“…Thus, there is a global time coordinate t ranging over a "time axis" R, and the spacetime metric has a very rigid time-symmetry with respect to this time-coordinate. We furthermore suppose that • the QFT admits a time-shift symmetry implemented by a continuous unitary group V t = e it H with generating Hamilton operator For more on the Reeh-Schlieder property, see [31,16,33,30].…”

Section: The D-ctc Condition In Qft On Globally Hyperbolic Spacetimesmentioning

confidence: 99%

The D-CTC Condition in Quantum Field Theory

Verch

2020

Progress and Visions in Quantum Theory in View of Gravity

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A condition proposed by David Deutsch to describe analogues of processes in the presence of closed timelike curves (D-CTC condition) in bipartite quantum systems is investigated within the framework of local relativistic quantum field theory. The main result is that in relativistic quantum field theory on spacetimes where closed timelike curves are absent, the D-CTC condition can nevertheless be fulfilled to arbitrary precision, under very general, model-independent conditions. Therefore, the D-CTC condition should not be taken as characteristic for quantum processes in the presence of closed timelike curves in the sense of general relativity. This report is a very condensed extract of the publication [35]. A new result showing that the D-CTC condition can be approximately fulfilled by entangled states is also presented.

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On the Reeh-Schlieder Property in Curved Spacetime

Cited by 39 publications

References 25 publications

Analytic Hadamard States, Calderón Projectors and Wick Rotation Near Analytic Cauchy Surfaces

Analytic Hadamard States, Calderón Projectors and Wick Rotation Near Analytic Cauchy Surfaces

Comments on a state-operator correspondence for the torus

The D-CTC Condition in Quantum Field Theory

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