A Bekenstein-type bound in QFT

TL;DR

This paper proves a model-independent, rigorous bound in quantum field theory relating the vacuum relative entropy of a localized state to its energy, extending Bekenstein-type bounds to QFT.

Contribution

It establishes a universal, first-principles bound on vacuum relative entropy in local QFT, analogous to Bekenstein bounds in gravitational contexts.

Findings

The vacuum relative entropy is bounded by 2π R times the state's energy.

The bound is model-independent and derived from fundamental principles.

It applies to translation covariant, local QFT on Minkowski spacetime.

Abstract

Let B be a spacetime region of width 2R > 0, and \phi a vector state localized in B. We show that the vacuum relative entropy of \phi, on the local von Neumann algebra of B, is bounded by 2\pi R-times the energy of the state \phi in B. This bound is model-independent and rigorous; it follows solely from first principles in the framework of translation covariant, local Quantum Field Theory on the Minkowski spacetime.