A reformulation of Schroedinger and Dirac equations in terms of observable local densities and electromagnetic fields: a step towards a new interpretation of quantum mechanics

It is shown that the Schroedinger equation, the 3-dimensional Dirac equation and the 4-dimensional Dirac equation can be transformed so as to eliminate all phase and gauge effects. Real local densities are defined and it is shown that these tensors obey real ''probabilistic equations'' which are equivalent to the equations of quantum mechanics. These new equations, which are explicity constructed, involve only local densities and the external electromagnetic field. New boundary conditions are also derived. The Aharonov-Bohm experiment is reinterpreted in the framework of this new formalism