Single-Particle Properties of a Two-Dimensional Fermi Liquid at finite Frequencies and Temperatures

We review the leading momentum, frequency and temperature dependences of the single particle self-energy and the corresponding term in the entropy of a two dimensional Fermi liquid (FL) with a free particle spectrum. We calculate the corrections to these leading dependences for the paramagnon model and the electron gas and find that the leading dependences are limited to regions of energy and temperature which decrease with decreasing number density of fermions. This can make it difficult to identify the frequency and temperature dependent characteristics of a FL ground state in experimental quantities in low density systems even when complications of band structure and other degrees of freedom are absent. This is an important consideration when the normal state properties of the undoped cuprate superconductors are analyzed.