 Then we can introduce notation of path ordering on this contour, by defining formula_34, where formula_35 is a permutation such that formula_36, and the plus and minus signs are for bosonic and fermionic operators respectively.Note that this is a generalization of time ordering.With this notation, the above time evolution is written as

formula_37

Where formula_22 corresponds to the time formula_19 on the forward branch of the Keldysh contour, and the integral over formula_40 goes over the entire Keldysh contour.