A Bekenstein-Type Bound in QFT

Source abstract

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