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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik
MP 17: Entropy in Quantum Field Theory
MP 17.1: Vortrag
Donnerstag, 2. September 2021, 16:30–16:55, H6
Relative entropy of coherent states on general CCR algebras — Henning Bostelmann1, •Daniela Cadamuro2, and Simone Del Vecchio2 — 1University of York, Department of Mathematics, York YO10 5DD, United Kingdom — 2Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103 Leipzig
The study of relative entropy between states in quantum field theory has recently attracted much attention in connection with the quantum null energy condition; usually one considers the vacuum and a coherent excitation, and the relative entropy with respect to a wedge algebra. In generalization of this, we study the relative entropy for a subalgebra of a generic CCR algebra between a general (possibly mixed) quasifree state and a coherent excitation of it. We give a formula for this entropy in terms of single-particle modular data. We also investigate changes of the relative entropy along subalgebras arising from an increasing family of symplectic subspaces, and study lower estimates for the second derivative of the relative entropy along this family, which replace the usual notion of convexity of the entropy. Our main input is a regularity condition for the family of subspaces (differential modular position) which generalizes the notion of half-sided modular inclusions. Examples include thermal states for the conformal U(1)-current.