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Diffusion on $κ$ -Minkowski space

Michele Arzano^*

Tomasz Trześniewski^†

Dipartimento di Fisica and INFN, “Sapienza” University of Rome, Piazzale Aldo Moro 2, 00185 Roma, Italy

Institute for Theoretical Physics, University of Wrocław, Plac Maxa Borna 9, 50-204 Wrocław, Poland

^*michele.arzano@roma1.infn.it
^†tomasz.trzesniewski@ift.uni.wroc.pl

Phys. Rev. D 89, 124024 – Published 20 June, 2014

DOI: https://doi.org/10.1103/PhysRevD.89.124024

Abstract

We study the spectral dimension associated with diffusion processes on Euclidean $κ$ -Minkowski space. We start by describing a geometric construction of the “Euclidean” momentum group manifold related to $κ$ -Minkowski space. On such space we identify various candidate Laplacian functions, i.e. deformed Casimir invariants, and calculate the corresponding spectral dimension for each case. The results obtained show a variety of running behaviors for the spectral dimension according to the choice of deformed Laplacian, from dimensional reduction to superdiffusion.

Article Text

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