An analysis of the Dicke model, N two-level atoms interacting with a single
radiation mode, is done using the Holstein-Primakoff transformation. The main
aim of the paper is to show that, changing the quantization axis with respect
to the common usage, it is possible to prove a general result either for N or
the coupling constant going to infinity for the exact solution of the model.
This completes the analysis, known in the current literature, with respect to
the same model in the limit of N and volume going to infinity, keeping the
density constant. For the latter the proper axis of quantization is given by
the Hamiltonian of the two-level atoms and for the former the proper axis of
quantization is defined by the interaction. The relevance of this result relies
on the observation that a general measurement apparatus acts using
electromagnetic interaction and so, one can states that the thermodynamic limit
is enough to grant the appearance of classical effects. Indeed, recent
experimental results give first evidence that superposition states disappear
interacting with an electromagnetic field having a large number of photons.