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arXiv · hep-th/9705010

Hausdorff dimension of a quantum string

S. Ansoldi·A. Aurilia·E. Spallucci
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Abstract

In the path integral formulation of quantum mechanics, Feynman and Hibbs noted that the trajectory of a particle is continuous but nowhere differentiable. We extend this result to the quantum mechanical path of a relativistic string and find that the ``trajectory'', in this case, is a fractal surface with Hausdorff dimension three. Depending on the resolution of the detecting apparatus, the extra dimension is perceived as ``fuzziness'' of the string world-surface. We give an interpretation of this phenomenon in terms of a new form of the uncertainty principle for strings, and study the transition from the smooth to the fractal phase.

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S. Ansoldi, A. Aurilia, E. Spallucci. 1997-05-03. Hausdorff dimension of a quantum string. https://doi.org/10.1103/physrevd.56.2352

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