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 CL and the red single lines are the linear response (propagator) RL. 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.
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