Validity of the rotating wave approximation in the driven Jaynes-Cummings model

In this paper we define, in the context of dynamical algebras, a set of operators that are suitable for studying any relevant quantity related to the two-level Jaynes-Cummings model (JCM). We study the usual JCM with and without the rotating wave approximation (RWA), and then we add the presence of an external field. In this last case we find that in the strong driving regime there are significant differences between the results obtained with the RWA and without it. This holds even for the case in which the usual requirements for applying the RWA without an external driving are fulfilled.