Statics and dynamics of charge fluctuations in the t-J model

The equation for the charge vertex gamma of the t-J model is derived and solved in leading order of a 1/N expansion, working directly in terms of Hubbard operators. Various quantities which depend crucially on gamma are then calculated, such as the lifetime and the transport lifetime of electrons due to a charge coupling to other degrees of freedom and the charge-charge correlation function. Our results show that the static screening of charges and the dynamics of charge fluctuations depend only weakly on J and are mainly determined by the constraint of having no double occupancies of sites.