  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.
