Relativistic Vlasov equation

A relativistic version of the Vlasov equation is applied to the study of infinite nuclear matter. The assumption is made that in hadronic matter the interactions are mediated by massive scalar and vector fields. The small amplitude oscillations around a stationary state are studied. Orthogonality and completeness relations and the energy weighted sum rule are obtained for longitudinal modes. The appearance of the zero sound mode and the distribution of the strength among the different modes are discussed. The scalar field couples to the energy excitations at high densities and for not too long wavelengths. The vector field couples strongly to the low energy excitations. The long wavelength and high density limits are study. (Author)