Hausdorff dimension of a quantum string
arXiv:hep-th/9705010 · doi:10.1103/PhysRevD.56.2352
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.
18 pages, non figures, ReVTeX 3.0, in print on Phys.Rev.D
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