  We develop a low-order conserving approximation for the interacting
resonant-level model (IRLM), and apply it to (i) thermal equilibrium, (ii)
nonequilibrium steady state, and (iii) nonequilibrium quench dynamics. Thermal
equilibrium is first used to carefully gauge the quality of the approximation
by comparing the results with other well-studied methods, and finding good
agreement for small values of the interaction. We analytically show that the
power-law exponent of the renormalized level width usually derived using
renormalization group approaches can also be correctly obtained in our approach
in the weak interaction limit. A closed expression for the nonequilibrium
steady-state current is derived and analytically and numerically evaluated. We
find a negative differential conductance at large voltages, and the exponent of
the power-law suppression of the steady-state current is calculated
analytically at zero-temperature. The response of the system to quenches is
investigated for a single-lead as well as for two-lead setup at finite voltage
bias at particle-hole symmetry using a self-consistent two-times Keldysh Green
function approach, and results are presented for the time-dependent current for
different bias and contact interaction strength.
