Reconstructing the formalism of quantum mechanics in the ``contextual objectivity" point of view

In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in such a way that it may be given an "objective reality". Here we use some ideas about the system dimensionality, taken from quant-ph/0101012, to propose a possible axiomatic approach to QM. In this approach the structure of QM appears as a direct consequence of the non-commutative character of the (classical geometrical) group of "knobs transformations", that relate between themselves the different positions of the measurement apparatus.

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