Number-Conserving Approaches for Atomic Bose-Einstein Condensates: An Overview

Assuming the existence of a Bose-Einstein condensate composed of the majority of a sample of ultracold, trapped atoms, perturbative treatments to incorporate the non-condensate fraction are common. Here we describe how this may be carried out in an explicitly number-conserving fashion, providing a common framework for the work of various authors; we also briefly consider issues of implementation, validity and application of such methods.