An interacting particles system revisited in the framework of the q-deformed algebra

We discuss the possibility of interpreting a q-deformed non-interacting system as incorporating the effects of interactions among its particles. This can be accomplished, for instance, in an ensemble of q-Boson by means of the virial expansion of a real gas in powers of the deformed parameter. The lowest-order virial coefficient reduces to the case of the standard, non-interacting Bose gas, while the higher-order virial coefficients contain effects arising from the interaction. The same picture can be drawn in a quantum-mechanical system where it is shown that the q-deformed momentum can be expanded in a series containing high-order powers of the standard quantum phase-space variables. Motivated by this result, we introduce, in the classical framework, a transformation relating the momentum of a free system to the momentum of an interacting system. It is shown that the canonical quantization applied to the interacting system implies a q-deformed quantization for the free system.