On Casimir force between two real metallic plates

The corrections to Casimir pressure (force) on two plates of real metal described by the dielectric constant of the Drude, Drude-Lorentz, Drude-Smith and plasma models at the finite temperature and conductivity are considered. We consider the contour integral lost in the Lifshitz formula and discuss inconsistencies for the corrections to the Casimir force given in the literature. Numerical and analytical results in the near and far zones are presented. The two first-order correction obtained due to the actual dielectric constant of the metal coincided with the literature data.