Role of scaling limits in the rigorous analysis of Bose-Einstein condensation

In the context of the rigorous analysis of Bose-Einstein condensation, recent achievements have been obtained in the form of asymptotic results when some appropriate scaling is performed in the Hamiltonian, and the limit of infinite number of particles is taken. In particular, two modified thermodynamic limits of infinite dilution turned out to provide an insight in this analysis, the so-called Gross-Pitaevskii limit and the related Thomas-Fermi limit. Here such scalings are discussed with respect to their physical and mathematical motivations and to the currently known results obtained within this framework. (C) 2007 American Institute of Physics.