We can write the above expression more succinctly by, purely formally, replacing each operator X ( t ) with a contour-ordered operator X ( c ) , such that c parametrizes the contour path on the time axis starting at t = 0 , proceeding to t = ∞ ∞ , and then returning to t = 0 . This path is known as the Keldysh contour. X ( c ) has the same operator action as X ( t ) (where t is the time value corresponding to c ) but also has the additional information of c (that is, strictly speaking X ( c 1 ) ≠ ≠ X ( c 2 ) if c 1 ≠ ≠ c 2 , even if for the corresponding times X ( t 1 ) = X ( t 2 ) ).