THE INFRARED CATASTROPHE - WHEN DOES IT TRASH FERMI-LIQUID THEORY

We give an historical discussion of the ''infrared catastrophe'' and the ''x-ray edge anomalies'' of Mahan associated with scatterers in a Fermi sea of electrons. The infrared catastrophe provides a perspicuous way into understanding the difficulties with many-body perturbation theory which have recently been discovered as a result of a study of high T(c) superconductivity, and we show how this ''catastrophe'' is avoided in some cases, but cannot be avoided in the one and 2-dimensional electron gas systems. Finally, we indicate the new type of theory which is necessary in the event of such a breakdown.