The resummation performed by the “direct steepest-descent” method at one-loop order, for the two-point correlation C. The blue single lines are the linear correlation C_L and the red single lines are the linear response (propagator) R_L. The double red lines in the first equality are the nonlinear response R (at that order), which contains an infinite series of bubble diagrams, and explicit substitution gives the series of diagrams shown in the second equality below.