New set of time-dependent Ginzburg-Landau equations for dirty superconductors near T/sub c/

A critical reexamination is given to the microscopic derivation of a set of time-dependent Ginzburg-Landau (TDGL) equations, for dirty superconductors near T/sub c/ (not assuming gaplessness), by Kramer and Watts-Tobin and by Schoen and Ambegaokar. The following improvements are first made: (i) A more general representation is used for the retarded 2 x 2 Green's function G/sup R/, valid in an arbitrary magnetic field; (ii) A ''static approximation'' for G/sup R/ is removed; (iii) An approximate gauge invariance is converted to an exact one, by some small changes in the equations for the order parameter and the charge density, in a way consistent with the approximation used. (iv) The simplifications of the collision integrals, based on a ''mutilated-collision-operator'' approximation, are shown to be also a direct consequence of the smallness of 1-T/T/sub c/. The set of equations is then tested against a local-charge-conservation law. A small violation is found, which leads to the discovery of an inconsistency in the truncation procedure used. Several new contributions are then found which leads to a new set of TDGL equations. This contains all the above improvements, and also satisfies a local-charge-conservation law essentially exactly. At least some of the new contributions are shown to be important in the energy range of the order of the gap frequency