SYMMETRY, RELATIVITY AND QUANTUM-MECHANICS

The objective is to investigate the physical meaning of a quantum prop erty - as yet unnoticed - stated as homogeneity of statistical ensembl es,,, which, together with the hypotheses of statistical determinism a nd of invariance of the formal structure under some group of transform ations, allows in a direct way to deduce the most general quantum-mech anical description in terms of density operators written as linear com binations of irreducible polarization tensors, a decomposition which p lays a considerable role in quantum optics and collision theory. The h ypothesis of invariance is analogous to the relativity principle, and the theory of quantum kinetic momentum is recovered in the special cas e of spherical symmetry, without additional assumptions. Thus these hy potheses give the physical meaning of the density-matrix formalism, wh ich 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-Zeilinge r argument or its future extensions.