Modular operator for null plane algebras in free fields

TL;DR

This paper analyzes the structure of null plane algebras in free quantum fields, demonstrating modular operator decomposition, validating a form of QNEC, and computing relative entropy for null cut algebras.

Contribution

It introduces a modular operator decomposition for null plane algebras in free fields and applies it to validate QNEC and compute relative entropy.

Findings

Modular operator decomposes into lightlike fibers.

A form of QNEC holds for free fields on null planes.

Relative entropy of null cut algebras is computed.

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.