Abstract
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.
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Holland, P.R. Geometry of dislocated de Broglie waves. Found Phys 17, 345–363 (1987). https://doi.org/10.1007/BF00733373
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DOI: https://doi.org/10.1007/BF00733373