The general cancellation of ladder graphs at finite temperature

In some cases, an important example being at finite temperature, extreme infrared, collinear, or light-cone behaviour may cause the usual loop expansion to break down. For some of these cases higher order ladder graphs can become important. In an earlier paper it was shown that, given a particular relation between a vertex and a self-energy function, the resummation of the ladder graphs simplifies significantly when other types of graphs are included in a consistent effective expansion. In this paper we show that this assumed relation is valid for a large class of vertex and self-energy functions at finite temperature.