A Deduced Feynman Rule for Calculating Retarded and Advanced Green   function in Closed Time Path Formalism
  Based on the closed time path formalism, a new Feynman rule for directly calculating the retarded and advanced Green functions is deduced. This Feynman rule is used to calculate the two-point self-energy and three-point vertex correction in $\phi^3$ theory. The generalized fluctuation-dissipation theorem for three-point nonlinear response function is verified. 
Jun Xiao and Enke Wang