  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 expectation
values of local observables are expected to relax to a Generalized Gibbs
Ensemble (GGE), constructed out of the conserved charges of the model.
Quenching to a free bosonic theory, it has been shown that the system indeed
relaxes to a GGE described by the momentum mode occupation numbers. We first
address the question whether the latter can be written directly in terms of
local charges and we find that, in contrast to the lattice case, this is not
possible in continuous field theories. We then investigate the less stringent
requirement of the existence of a sequence of truncated local GGEs that
converges to the correct steady state, in the sense of the expectation values
of the local observables. While we show that such a sequence indeed exists, in
order to unequivocally determine the so-defined GGE, we find that information
about the expectation value of the recently discovered quasi-local charges is
in the end necessary, the latter being the suitable generalization of the local
charges while passing from the lattice to the continuum. Lastly, we study the
locality properties of the GGE and show that the latter is completely
determined by the knowledge of the expectation value of a countable set of
suitably defined quasi-local charges.
