Electromagnetic response of the electron gas and the thermal Casimir pressure anomaly

In this paper, a review of the nonlocal electromagnetic response functions for the degenerate electron gas, computed within standard perturbation theory, is given. These expressions due to Lindhard, Klimontovich and Silin are used to re-analyze the Casimir interaction between two thick conducting plates in the leading order at high temperatures (zeroth term of Matsubara series). Up to small corrections that we discuss, the results of the conventional Drude model are confirmed. The difference between longitudinal and transverse permittivities (or polarization tensors) yields the Landau (orbital) diamagnetism of the electron gas.