How to Measure the Fractal Geometry of the Relativistic Fermion Propagator

Abstract

We study the geometry of propagation of relativistic fermions. We propose how to measure its quantum mechanical length. Numerical lattice results for the free propagator of Dirac-Wilson fermions yield Hausdorff dimension d_H=2 for the unit-matrix component and d_H=1 for any gamma-matrix component. A possible generalization when matter interacts with radiation is discussed.

Comments: 14 pages, LaTeX + 6 figures, PS