Entanglement and Quantum Information in Quantum Field Theory

We study entanglement and its connection to thermalization in the context of quantum field theory. Entanglement is an intrinsically non--local phenomenon, which makes it particularly difficult to study in continuous field theoretic systems. Thus, the measures of entanglement, such as entanglement entropy, are notoriously difficult to calculate even for weakly coupled models. In this project we aim to develop a novel theoretical framework to calculate entanglement perturbatively, expanding in small parameter. To that end we propose to study local structure of modular Hamiltonian and variation of the entanglement entropy with respect to UV--cutoff scale. These results will be subsequently used to calculate time evolution of the entanglement entropy following a quantum quench.