General cancellation of ladder graphs at finite temperature

some cases, an important example being at finite temperature, extreme infrared, collinear, or light-cone behavior may cause the usual loop-expansion to break down. For some of these cases higher order ladder graphs can become important. In all 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.