Modular Hamiltonians on the null plane and the Markov property of the vacuum state
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Publication:5369072
DOI10.1088/1751-8121/AA7EAAzbMATH Open1376.81066arXiv1703.10656OpenAlexW2604578214WikidataQ64038432 ScholiaQ64038432MaRDI QIDQ5369072
Author name not available (Why is that?)
Publication date: 12 October 2017
Published in: (Search for Journal in Brave)
Abstract: We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non locally outside the null plane. We regain this result in greater generality using more abstract tools on algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.
Full work available at URL: https://arxiv.org/abs/1703.10656
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