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.

arXiv comment35 pages, 2 figures

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• From Quantum Relative Entropy to the Semiclassical Einstein Equations
• Modular Hamiltonian for fermions of small mass
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• Entanglement Entropy in CFT and Modular Nuclearity