Spectral dimension of kappa space-time

Abstract

We calculate the spectral dimension associated with a diffusion equation in the κ-deformed space-time. We setup this deformed diffusion equation using the Casimir of the undeformed κ-Poincare algebra DμDμ, which is the Laplacian of the underlying space. The κ-diffusion equation is solved perturbatively and the solution is used to derive the spectral dimension. It is found that the effective dimension is same as the topological dimension for large diffusion times and decreases with the probe length.