Resummation of infrared divergencies in the theory of atomic Bose gases

We present a general strong-coupling approach for the description of an atomic Bose gas beyond the Bogoliubov approximation, when infrared divergences start to occur that need to be resummed exactly. We consider the determination of several important physical properties of the Bose gas, namely the chemical potential, the contact, the speed of sound, the condensate density, the effective interatomic interaction and the three-body recombination rate. It is shown how the approach can be systematically improved with renormalization-group methods and how it reduces to the Bogoliubov theory in the weak-coupling limit.