Exact Results in Quantum Theory

Via the Araki-Uhlmann formula, the Tomita-Takesaki theory of modular flows of von Neumann algebras can be used to compute relative entropy also in situations where the von Neumann entropy is infinite, such as for the local algebras of quantum field theory. The main ingredient in this formula is the relative modular operator (or the relative modular Hamiltonian, its logarithm), which depends on the states and (in QFT) the spacetime region under consideration, and which is only known in a handful of examples. I will present some new modular Hamiltonians and the results that one obtains for the relative entropy in these cases, as well as generalizations to other entropy measures and a no-go result. Joint work with subsets of {Albert Much, Kyriakos Papadopoulos, Edoardo D'Angelo, Stefano Galanda, Paolo Meda, Daniela Cadamuro, Christoph Minz, Guillem Perez-Nadal, Leonardo Sangaletti, Dimitrios Katsinis, Jan Mandrysch}.