A Bekenstein-type bound in QFT

Abstract

Let B be a spacetime region of width 2R > 0, and ϕa vector state localized in B. We show that the vacuum relative entropy of ϕ, on the local von Neumann algebra of B, is bounded by 2πR-times the energy of the state ϕin 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.

16 pages