A systematic study of entanglement entropy in relativistic quantum field theory is discussed. For the case of a 1+1-dimensional critical system, whose continuum limit is a conformal field theory with central charge c, the result S_A≈(c/3) log(l) is re-derived, and it is extended to many other cases: finite systems, finite temperatures, and when A consists of an arbitrary number of disjoint intervals. For such a system away from its critical point, when the correlation length ξ is large but finite, the result S_A≈N(c/6)log(ξ) is shown, where N is the number of boundary points of A. I will finally discuss the unitary relaxation from a non-equilibrium initial state, showing that both CFT and the exact solution of an integrable model lead, contrarily to the ground state case to an extensive entanglement entropy. These findings are explained in terms of causality.

ITP, Amsterdam