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.

14 pages, LaTeX + 6 figures, PS

References in corpus (4)

• Transfer Matrix Formalism for Two-Dimensional Quantum Gravity and Fractal Structures of Space-time
• A Universal Fractal Structure of 2D Quantum Gravity for c > 1
• Measuring the Hausdorff Dimension of Quantum Mechanical Paths
• Fractal Structure in Two-Dimensional Quantum Regge Calculus

Cited by in corpus (1)

• Hausdorff dimension of a particle path in a quantum manifold