Keldysh Ginzburg-Landau action of fluctuating superconductors

We derive Ginzburg-Landau action by systematically integrating out electronic degrees of freedom in the framework of the Keldysh nonlinear sigma-model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal $\mathrm{\Delta }$-dependent contribution to the diffusion constant, which leads, for example, to Maki-Thompson corrections. It also exhibits an anomalous Gor’kov-Eliashberg coupling between $\mathrm{\Delta }$ and the scalar potential, as well as a peculiar nonlocal nonlinear term. The action is gauge invariant and satisfies the fluctuation dissipation theorem. It may be employed e.g. for calculation of higher moments of the current fluctuations.