The lattice dynamics of hcp crystalline 4 He is studied at zero temperature and for two different densities ͑near and far from melting͒, using a ground-state path-integral quantum Monte Carlo technique. The complete phonon dispersion is obtained, with particular attention to the separation of optic and acoustic branches and to the identification of transverse modes. Our study also sheds light on the residual coherence affecting quasiparticle excitations in the intermediate momentum region, in between the phonon and nearly free-particle regimes.The lattice dynamics of solid 4 He has long been considered a major challenge to ab initio calculations, due to the strong anharmonicity of this highly quantum solid. Many calculations have been performed within the self-consistent phonon ͑SCP͒ approximation, 1,2 which however may be rather unsatisfactory, due to the magnitude of anharmonic effects. A significant improvement has been made possible by the application of a variational quantum Monte Carlo ͑QMC͒ approach, based on the shadow wave function formalism, to bcc 3 He ͑Ref. 3͒ and to hcp 4 He. 4 The variational nature of this approach, however, makes it not fully suitable at high energy where optical or zone-boundary longitudinal excitations exhibit broad multiphonon features. In this spectral regime, the calculation of the full dynamic structure factor is therefore in order. QMC techniques based on path integrals allow quite naturally for the calculation of imaginarytime correlation functions from which various spectral functions, such as the dynamic structure factor, can be obtained upon analytical continuation. This technique has been successfully demonstrated for superfluid 4 He, 5,6 as well as for the bcc crystalline phases of 4 He ͑Refs. 7 and 8͒ and 3 He. 9 In the latter studies the spectrum of the transverse excitations has also been obtained, albeit in the one-phonon approximation only. 2 In this work we present an extensive study of the dynamical properties of hcp 4 He at zero temperature, performed by estimating the dynamic structure factor from ground-state path-integral simulations. 6,10,11 This technique allows us to parallel to some extent the procedure followed experimentally to map phonon dispersions from the measured neutron scattering. In the long-wavelength region-well approximated by a phonon picture of the collective density excitations-we thus obtain longitudinal as well as transverse modes for both acoustic and optical branches. For higher wave-vectors we analyze the dynamic structure factor in terms of corrections to the so-called impulse approximation, 12 finding a coherent response which is peculiar of both superfluid and solid helium.In Sec. I we give an introductory account of the phonon theory of long-wavelength excitations in solids. In Sec. II the reader is provided with an outline of the numerical methods adopted in this work. In Sec. III we report on the analysis of our QMC results both in the phonon regime and in the intermediate momentum region. Sec. IV is finally devoted to a few c...