  We determine the thermodynamic properties and the spectral function for a
homogeneous two-dimensional Fermi gas in the normal state using the
Luttinger-Ward, or self-consistent T-matrix, approach. The density equation of
state deviates strongly from that of the ideal Fermi gas even for moderate
interactions, and our calculations suggest that temperature has a pronounced
effect on the pressure in the crossover from weak to strong coupling,
consistent with recent experiments. We also compute the superfluid transition
temperature for a finite system in the crossover region. There is a pronounced
pseudogap regime above the transition temperature: the spectral function shows
a Bogoliubov-like dispersion with back-bending, and the density of states is
significantly suppressed near the chemical potential. The contact density at
low temperatures increases with interaction and compares well with both
experiment and zero-temperature Monte Carlo results.
