What Is Wrong with Paramagnons?

Systems with itinerant fermions close to a zero temperature quantum phase transition like the high temperature superconductors exhibit unusual non Fermi liquid properties. The interaction of the long range and low energy fluctuations of the incipient order with the fermions modify the dynamical properties of the fermions strongly by inducing effective long range interactions. Close to the transition the interaction of the order parameter fluctuations becomes important. In this paper we discuss the physics of the non Gaussian order parameter fluctuations on the electronic spectrum and illustrate their effect by considering the charge density wave transition. We show how to generalize the one dimensional problem to the phase fluctuations of a two dimensional superconductor.