A Bekenstein-Type Bound in QFT

Abstract

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