ON AN APPROXIMATE FORM OF THE COUPLED EQUATIONS OF THE ORDER PARAMETER WITH THE WEAK ELECTROMAGNETIC FIELD FOR THE IDEAL SUPERCONDUCTOR

A simplified derivation of the macroscopic electrodynamic equations of Umezawa, Mancini et al. for superconductors is given in the framework of the closed time path Green's functions (CTPGF) using generalized Ward-Takahashi identities. It is shown that the forms of the equations obtained are the same for both thermoequilibrium and nonequilibrium stationary states provided the eletromagnetic field is weak and its effect on the modulus of the order parameter can be neglected. The statistical behavior of the states is completely specified in the equations by parameters which can be calculated by the method of CTPGF.