The Reeh–Schlieder property for ground states

Jäkel, Christian

doi:10.1002/andp.200310012

Cited by 3 publications

(3 citation statements)

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“…We note that for quantum fields of spin less than 2 the Reeh-Schlieder theorem has been proven, under various circumstances, on a number of curved backgrounds -see e.g. [79,80,81,82,83,84,85]. The Reeh-Schlieder theorem is often viewed as a statement about the analyticity properties of the n-pt functions of state vectors in D c .…”

Section: The Reeh-schlieder Theoremmentioning

confidence: 95%

On cosmic hair and "de Sitter breaking" in linearized quantum gravity

Morrison

2013

Preprint

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We quantize linearized Einstein-Hilbert gravity on de Sitter backgrounds in a covariant gauge. We verify the existence of a maximally-symmetric (i.e. de Sitter-invariant) Hadamard state Ω for all globally hyperbolic de Sitter backgrounds in all spacetime dimensions D ≥ 4 by constructing the state's 2-point function in closed form. This 2-pt function is explicitly maximally symmetric. We prove an analogue of the Reeh-Schlieder theorem for linearized gravity. Using these results we prove a cosmic no-hair theorem for linearized gravitons: for any state in the Hilbert space constructed from Ω, the late-time behavior of local observable correlation functions reduces to those of Ω at an exponential rate with respect to proper time. We also provide the explicitly maximally-symmetric graviton 2-pt functions in a class of generalized de Donder gauges suitable for use in non-linear perturbation theory. Along the way we clarify a few technical aspects which led previous authors to conclude that these 2-pt functions do not exist.

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Section: The Reeh-schlieder Theoremmentioning

confidence: 95%

On cosmic hair and "de Sitter breaking" in linearized quantum gravity

Morrison

2013

Preprint

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“…Another property of quantum field theories derivable from the Reeh-Schlieder theorem is the entanglement of the vacuum. I will not insist on this aspect here, as it has been extensively discussed in [52,53]. However, due to this newly proved connection, topology appears to be a useful tool for the description of the entanglement of vacuum in quantum field theories.…”

Section: Mayer-vietoris and Reeh-schliedermentioning

confidence: 99%

Entanglement, space-time and the Mayer-Vietoris theorem

Patrascu

2017

J. High Energ. Phys.

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Entanglement appears to be a fundamental building block of quantum gravity leading to new principles underlying the nature of quantum space-time. One such principle is the ER-EPR duality. While supported by our present intuition, a proof is far from obvious. In this article I present a first step towards such a proof, originating in what is known to algebraic topologists as the Mayer-Vietoris theorem. The main result of this work is the re-interpretation of the various morphisms arising when the Mayer-Vietoris theorem is used to assemble a torus-like topology from more basic subspaces on the torus in terms of quantum information theory resulting in a quantum entangler gate (Hadamard and c-NOT).

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“…It is important to note that although the original arguments used in the derivation of the Reeh-Schlieder theorem use global symmetry properties of the vacuum state, in general curved spacetimes there is no guarantee that such symmetries exist [68]. Therefore, it was an actual challenge to obtain this results in curved spacetimes, which makes Sanders' work even more impressive.…”

Section: Chapter the Reeh-schlieder Theoremmentioning

confidence: 99%

Functorial formulation of Algebraic Quantum Field Theory in curved spacetimes and the Reeh-Schlieder Theorem

Estêves¹

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First, I would like to thank my supervisor Prof. Dr. João Carlos Alves Barata for providing me with this project and for all the support and feedback given. His trust in me was essential for me to believe that I could finish this work.The research group was essential for me to get an extra feedback on my presentations. The insights of my colleagues would always make me think about something that I had not thought of before and were crucial for the development of this project. So, here my thanks goes to Ricardo Corrêa, Victor Chabu, Gabriel Barbosa, Lissa Campos, Marcos Brum, and to all the undergraduate students that participated.I thank all my friends in the Physics Institute for bringing joy to my day-to-day life and for sharing their insecurities regarding the academic life, which is not easy for anyone. So, thanks Caio, Gabriel, Giulio, Brenda, Carol, Felipe, Ivan, Lissa and Leandro for being part of my life. I admire you all, and spending time with you inspires me every day.I want to thank Agnes, whose company in the first months of the masters made it much easier for me to adapt to São Paulo and my new routine. Also, thanks to Mari,

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The Reeh–Schlieder property for ground states

Abstract: Abstract. Recently it has been shown that the Reeh-Schlieder property w.r.t. thermal equilibrium states is a direct consequence of locality, additivity and the relativistic KMS condition. Here we extend this result to ground states.

Cited by 3 publications

References 11 publications

On cosmic hair and "de Sitter breaking" in linearized quantum gravity

On cosmic hair and "de Sitter breaking" in linearized quantum gravity

Entanglement, space-time and the Mayer-Vietoris theorem

Functorial formulation of Algebraic Quantum Field Theory in curved spacetimes and the Reeh-Schlieder Theorem

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