Modular operator for null plane algebras in free fields

Abstract

We consider the algebras generated by observables in quantum field theory localized in regions in the null plane. For a scalar free field theory, we show that the one-particle structure can be decomposed into a continuous direct integral of lightlike fibres, and the modular operator decomposes accordingly. This implies that a certain form of QNEC is valid in free fields involving the causal completions of half-spaces on the null plane (null cuts). We also compute the relative entropy of null cut algebras with respect to the vacuum and some coherent states.

35 pages, 2 figures

References in corpus (4)

• Relative entropy and the Bekenstein bound
• Entropy on a null surface for interacting quantum field theories and the Bousso bound
• Lectures on quantum energy inequalities
• Entropy of Coherent Excitations

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• Relative Entropy in de Sitter is a Noether Charge
• Relative entropy of an interval for a massless boson at finite temperature
• From Quantum Relative Entropy to the Semiclassical Einstein Equations
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• A numerical analysis of Araki-Uhlmann relative entropy in Quantum Field Theory
• Petz-Rényi relative entropy in QFT from modular theory
• Entanglement Entropy in CFT and Modular Nuclearity