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 σ -model of disordered superconductors. The resulting Ginzburg-Landau functional contains a nonlocal Δ -dependent contribution to the diffusion constant, which leads, for example, to Maki-Thompson corrections. It also exhibits an anomalous Gor'kov-Eliashberg coupling between Δ 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.