## ABSTRACT

In Sec. 12.3 we briefly discussed the linear interaction between the transverse part of a classical electromagnetic field and a system of charged particles (electrons). At high frequencies we concluded that the main contribution to the many-body conductivity tensor came from the diamagnetic interaction. In the superconducting state the diamagnetic fieldelectron interaction is the dominating one in the weak-field limit [212, 45, 8, 107, 108]. The diamagnetic interaction gives a spatially local relation between the microscopic electron current density and the transverse vector potential, the proportionality factor being −(e2/m)N0(r), where N0(r) is the local many-body electron density. If one assumes that this density is homogeneous, the transverse photon acquires an effective mass (proportional to the plasma frequency of the electron system), and the transverse vector potential obeys the Proca equation since the transverse vector potential is gauge invariant.