The power of AQFT: the area law for entropy of localized quantum matter

The algebraic approach to QFT, which for several decades has enriched QFT with structural theorems, has recently shown its utility in various constructions of actual interest. In these lecture notes I explain how AQFT (in particular the modular theory of operator algebras) implies paradigmatic conceptual and mathematical changes while fully preserving the physical principles which underly QFT. As an illustration of actual interest I use holography on null-surfaces and the ensuing area law for entropy of localized matter in the vacuum state.