Physics – High Energy Physics – High Energy Physics - Lattice
Scientific paper
1995-01-17
Phys.Lett. A199 (1995) 299
Physics
High Energy Physics
High Energy Physics - Lattice
uuencoded and compressed shell archive file. 8 pages with 7 figures
Scientific paper
10.1016/0375-9601(95)00127-O
We measure the propagator length in imaginary time quantum mechanics by Monte Carlo simulation on a lattice and extract the Hausdorff dimension $d_{H}$. We find that all local potentials fall into the same universality class giving $d_{H}=2$ like the free motion. A velocity dependent action ($S \propto \int dt \mid \vec{v} \mid^{\alpha}$) in the path integral (e.g. electrons moving in solids, or Brueckner's theory of nuclear matter) yields $d_{H}=\frac{\alpha }{\alpha - 1}$ if $\alpha > 2$ and $d_{H}=2$ if $\alpha \leq 2$. We discuss the relevance of fractal pathes in solid state physics and in $QFT$, in particular for the Wilson loop in $QCD$.
Kr{ö}ger Helmut
Lantagne S.
Moriarty K. J. M.
Plache B.
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