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We study the quench dynamics in continuous relativistic quantum field theory,more specifically the locality properties of the large time stationary state.After a quantum quench in a one-dimensional integrable model, the expectationvalues of local observables are expected to relax to a Generalized GibbsEnsemble (GGE), constructed out of the conserved charges of the model.Quenching to a free bosonic theory, it has been shown that the system indeedrelaxes to a GGE described by the momentum mode occupation numbers. We firstaddress the question whether the latter can be written directly in terms oflocal charges and we find that, in contrast to the lattice case, this is notpossible in continuous field theories. We then investigate the less stringentrequirement of the existence of a sequence of truncated local GGEs thatconverges to the correct steady state, in the sense of the expectation valuesof the local observables. While we show that such a sequence indeed exists, inorder to unequivocally determine the so-defined GGE, we find that informationabout the expectation value of the recently discovered quasi-local charges isin the end necessary, the latter being the suitable generalization of the localcharges while passing from the lattice to the continuum. Lastly, we study thelocality properties of the GGE and show that the latter is completelydetermined by the knowledge of the expectation value of a countable set ofsuitably defined quasi-local charges.

Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories