Geometry of dislocated de Broglie waves

The geometrical structures implicit in the de Broglie waves associated with a relativistic charged scalar quantum mechanical particle in an external field are analyzed by employing the ray concept of the causal interpretation. It is shown how an osculating Finslerian metric tensor, a torsion tensor, and a tetrad field define respectively the strain, the dislocation density, and the Burgers vector in the natural state of the wave, which is a non-Riemannian space of distant parallelism. A quantum torque determined by the quantum potential is introduced and the example of a screw dislocated wave is discussed.