  Motivated by a large number of recent magnetotransport studies we have
revisited the problem of the microscopic calculation of the quasiparticle
effective mass in a paramagnetic two-dimensional (2D) electron liquid (EL). Our
systematic study is based on a generalized $GW$ approximation which makes use
of the many-body local fields and takes advantage of the results of the most
recent QMC calculations of the static charge- and spin-response of the 2D EL.
We report extensive calculations for the many-body effective mass enhancement
over a broad range of electron densities. In this respect we critically examine
the relative merits of the on-shell approximation, commonly used in
weak-coupling situations, {\it versus} the actual self-consistent solution of
the Dyson equation. We show that already for $r_s \simeq 3$ and higher, a
solution of the Dyson equation proves here necessary in order to obtain a well
behaved effective mass. Finally we also show that our theoretical results for a
quasi-2D EL, free of any adjustable fitting parameters, are in good qualitative
agreement with some recent measurements in a GaAs/AlGaAs heterostructure.
