Symmetry, relativity and quantum mechanics

The objective is to investigate the physical meaning of a quantum property - as yet unnoticed - stated as 'homogeneity of statistical ensembles', which, together with the hypotheses of statistical determinism and of invariance of the formal structure under some group of transformations, allows in a direct way to deduce the most general quantum-mechanical description in terms of density operators written as linear combinations of irreducible polarization tensors, a decomposition which plays a considerable role in quantum optics and collision theory. The hypothesis of invariance is analogous to the relativity principle, and the theory of quantum kinetic momentum is recovered in the special case of spherical symmetry, without additional assumptions. Thus these hypotheses give the physical meaning of the density-matrix formalism, which is derived as a direct theory of quantum probabilities, dispensing with the usual postulates concerning amplitudes. As a contribution to the interpretation debate of quantum theory, it is suggested that the polarization tensors should be considered as 'new elements of physical reality which cannot be ruled out by the Greenberger-Horne-Zeilinger argument or its future extensions