 We can write the above expression more succinctly by, purely formally, replacing each operator formula_20 with a contour-ordered operator formula_21 , such that formula_22 parametrizes the contour path on the time axis starting at formula_23, proceeding to formula_24, and then returning to formula_23.This path is known as the Keldysh contour.formula_26 has the same operator action as formula_20 (where formula_19 is the time value corresponding to formula_22) but also has the additional information of formula_22 (that is, strictly speaking formula_31 if formula_32, even if for the corresponding times formula_33).