  The violent relaxation and the metastable states of the Hamiltonian
Mean-Field model, a paradigmatic system of long-range interactions, is studied
using a Hamiltonian formalism. Rigorous results are derived algebraically for
the time evolution of selected macroscopic observables, e.g., the global
magnetization. The high and low energy limits are investigated and the
analytical predictions are compared with direct $N$-body simulations. The
method we use enables us to re-interpret the out-of-equilibrium phase
transition separating magnetized and (almost) unmagnetized regimes.
