KMS conditions for 4-point Green functions at finite temperature

We study the 4-point function in the Keldysh formalism of the closed time path formulation of real time finite temperature field theory. We derive the KMS conditions for these functions and discuss the number of 4-point functions that are independent. We define a set of `physical' functions which are linear combinations of the usual Keldysh functions. We show that these functions satisfy simple KMS conditions. In addition, we consider a set of integral equations which represent a resummation of ladder graphs. We show that these integral equations decouple when one uses the physical functions that we have defined. We discuss the generalization of these results to QED.