Area Law for Localization-Entropy in Local Quantum Physics

The previously developed algebraic lightfront holography is used in conjunction with the tensor splitting of the chiral theory on the causal horizon. In this way a universal area law for the entanglement entropy of the vacuum relative to the split (tensor factorized) vacuum is obtained. The universality of the area law is a result of the kinematical structure of the properly defined lightfront degrees of freedom. We consider this entropy associated with causal horizon of the wedge algebra in Minkowski spacetime as an analog of the quantum Bekenstein black hole entropy, similar to the way in which the Unruh temperature for the wedge algebra may be viewed as an analog in Minkowski spacetime of the Hawking thermal behavior. My more recent preprint hep-th/20202085 presents other aspects of the same problem. 1 Introductory remarks “Localization Entropy” [1][2] is an entropy which has its origin in the fact that in local quantum physics (in distinction to quantum mechanics) the vacuum, if restricted to a causally closed algebra with a nontrivial causal complement, behaves as a thermal state [7]. The best known illustration is the vacuum restricted to the algebra of quantum matter localized in a Rindler wedge which leads to the planar Unruh situation i.e. a thermal state with a Hawking temperature (which depends on the horizon-generating acceleration in the Unruh Gedankenexperiment) which is accompanied by thermal radiation [6]. Whereas the thermal aspect of such a situation is related to the general observation that spacetime restrictions of globally pure states in QFT to regions with a nontrivial This is the formulation of QFT without the use of field-coordinatizations.