Würzburg Seminar on Quantum Field Theory and Gravity

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One of the most popular entanglement measures is the entanglement entropy, which is expressed in terms of the relative entropy. In quantum mechanics, these entropies can be formulated in terms of density matrices. In the setting of quantum field theory, however, density matrices are typically ill-defined and one needs to resort to the modular theory of Tomita-Takesaki to obtain a mathematically clean formulation. In this talk I will review the formulation of the entanglement entropy and some results on modular theory and relative entropy, including some work in progress on direct integral decompositions.