THE "INFRARED CATASTROPHE": WHEN DOES IT TRASH FERMI LIQUID THEORY?

Abstract

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 Tc 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.