04 02 1 v 1 1 0 A pr 1 99 7 Bohmian Mechanics Revisited

We consider the problem of whether there are deterministic theories describing the evolution of an individual physical system in terms of the definite trajectories of its constituent particles and which stay in the same relation to Quantum Mechanics as Bohmian Mechanics but which differ from the latter for what concerns the trajectories followed by the particles. We discuss the transformation properties of such theories under the transformations of the extended Galilei group and we point out that, in a context like the one we are interested in, one can put forward various requests that we refer to as physical and genuine covariance and invariance. We show that there are infinitely many inequivalent (from the point of view of the trajectories) bohmian-like theories reproducing the predictions of Quantum Mechanics and which satisfy the most restrictive invariance requirements which can be imposed on them. This raises some interesting questions about the meaning of Bohmian Mechanics.