Abstract:
This talk is about the computation of the relative entropy associated to an interval between a thermal state and a coherent excitation of itself in the bosonic U(1)-current model, namely the (derivative of the) chiral boson. The main goal is to compute the corresponding relative entropy of Araki. For this purpose I will start by presenting some well-known facts on the algebra of Canonical Commutation Relations as well as more recent results of R. Longo and collaborators on the entropy of subspaces and of Bostelmann, Cadamuro and Del Vecchio on the relative entropy of non-pure states (by purification) such as thermal states. Then, by extending previous results of Borchers and Yngvason (which will be briefly recalled) it will be possible to make use of the full PSL(2,R) symmetries and hopefully become clear how to arrive at the sought relative entropy. Such entropy entails both a Bekenstein-like bound and a QNEC-like bound, which deserve further investigation. The talk is based on work in progress with Gabriel Palau.