  In contrast to lattice systems where powerful numerical techniques such as
matrix product state based methods are available to study the non-equilibrium
dynamics, the non-equilibrium behaviour of continuum systems is much harder to
simulate. We demonstrate here that Hamiltonian truncation methods can be
efficiently applied to this problem, by studying the quantum quench dynamics of
the 1+1 dimensional Ising field theory using a truncated free fermionic space
approach. After benchmarking the method with integrable quenches corresponding
to changing the mass in a free Majorana fermion field theory, we study the
effect of an integrability breaking perturbation by the longitudinal magnetic
field. In both the ferromagnetic and paramagnetic phases of the model we find
persistent oscillations with frequencies set by the low-lying particle
excitations not only for small, but even for moderate size quenches. In the
ferromagnetic phase these particles are the various non-perturbative confined
bound states of the domain wall excitations, while in the paramagnetic phase
the single magnon excitation governs the dynamics, allowing us to capture the
time evolution of the magnetisation using a combination of known results from
perturbation theory and form factor based methods. We point out that the
dominance of low lying excitations allows for the numerical or experimental
determination of the mass spectra through the study of the quench dynamics.
