Kinetic Equation with Relativistic Interaction Corrections for a Plasma

Using the formalism of Weinstock, a master equation for a momentum-dependent interaction is given. An exact kinetic equation (to lowest order in $e^2$) for a homogeneous plasma in which relativistic interaction corrections to order ${\left(\frac{v}{c}\right)}^2$ are included is also given. It is readily shown that with the relativistic approximation the well-known divergences of the kinetic equation are removed without invoking cutoffs (as is also true in the nonrelativistic case given by Weinstock).