Uniqueness of paths in quantum mechanics

The constraints imposed by relativistic covariance on the law of motion of fermions in the trajectory interpretation of quantum mechanics are examined. It is found that the quantum current satisfies a uniqueness property that fixes the guidance law. This in turn fixes the nonrelativistic equation which generally differs from that originally given by de Broglie and Bohm for electrons. These results extend to Bohm’s noncovariant many-body theory. The demonstration does not exclude other guidance equations and this is shown by the explicit construction of an alternative Lorentz covariant many-body theory possessing future-causal space-time paths.