We address the question which additional information on the source shape and
dynamics can be extracted from three-particle Bose-Einstein correlations. For
chaotic sources the true three-particle correlation term is shown to be
sensitive to the momentum dependence of the saddle point of the source and to
its asymmetries around that point. For partially coherent sources the
three-pion correlator allows to measure the degree of coherence without
contamination from resonance decays. We derive the most general Gaussian
parametrization of the two- and three-particle correlator for this case and
discuss the space-time interpretation of the corresponding parameters.Comment: 16 pages, to be published in Phys. Rev.
