  The cumulant expansion is a powerful approach for including correlation
effects in electronic structure calculations beyond the GW approximation.
However, current implementations are incomplete since they ignore terms that
lead to partial occupation numbers and satellites both above and below the
Fermi energy. These limitations are corrected here with a generalized cumulant
approximation that includes both particle and hole contributions within a
retarded Green's function formalism. The computational effort is still
comparable to GW, and the method can be extended easily to finite temperature.
The approach is illustrated with calculations for the homogeneous electron gas
and comparisons to experiment and other methods.
