Dimensions of relativistic quantum mechanical paths

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Abstract
The notion of the dimension of a relativistic quantum mechanical path is illustrated. An elementary introduction to the concept of a fractal curve allows the discussion of the evolution of the quantum mechanical wave packet for free particles in terms of Hausdorff dimensions of quantum ‘‘trajectories.’’ The results of a previous work by Abbott and Wise can be generalized to relativistic quantum mechanics of spin‐1/2 particles in the Foldy–Wouthuysen representation. A further extension to spin‐zero particles is briefly outlined. By simple considerations, an understanding of the notion of a Hausdorff dimension and its values can be introduced.

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