  The Gross-Pitaevskii equation has been extremely successful in the theory of
weakly-interacting Bose-Einstein condensates. However, present-day experiments
reach beyond the regime of its validity due to the significant role of
correlations. We review a method of tackling the dynamics of correlations in
Bose condensed gases, in terms of noncommutative cumulants. This new approach
has a wide range of applicability in the areas of current interest, e.g. the
production of molecules and the manipulation of interactions in condensates. It
also offers an interesting perspective on the classical-field methods for
partly condensed Bose gases.

Condensed Matter;Atomic Physics;Quantum Physics