Hausdorff dimension of a particle path in a quantum manifold
- Frankfurt Institute for Advanced Studies (FIAS), Institut fuer Theoretische Physik, Johann Wolfgang Goethe-Universitaet, Ruth-Moufang-Strasse 1, 60438 Frankfurt am Main (Germany)
After recalling the concept of the Hausdorff dimension, we study the fractal properties of a quantum particle path. As a novelty we consider the possibility for the space where the particle propagates to be endowed with a quantum-gravity-induced minimal length. We show that the Hausdorff dimension accounts for both the quantum mechanics uncertainty and manifold fluctuations. In addition the presence of a minimal length breaks the self-similarity property of the erratic path of the quantum particle. Finally we establish a universal property of the Hausdorff dimension as well as the spectral dimension: They both depend on the amount of resolution loss which affects both the path and the manifold when quantum gravity fluctuations occur.
- OSTI ID:
- 21503963
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 83, Issue 2; Other Information: DOI: 10.1103/PhysRevD.83.024017; (c) 2011 American Institute of Physics; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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