  We investigate two theoretical pseudomagnon-based models for a bilayer
quantum Hall system (BQHS) at total filling factor $\nu_t = 1$. We find a
unifying framework which elucidates the different approximations that are made.
We also consider the effect of an in-plane magnetic field in BQHSs at $\nu_t =
1$, by deriving an equation for the ground state energy from the underlying
microscopic physics. Although this equation is derived for small in-plane
fields, its predictions agree with recent experimental findings at stronger
in-plane fields, for low electron densities. We also take into account
finite-temperature effects by means of a renormalisation group analysis, and
find that they are small at the temperatures that were investigated
experimentally.
