Diffusion on $\kappa$-Minkowski space

Abstract

We study the spectral dimension associated with diffusion processes on Euclidean $\kappa$-Minkowski space. We start by describing a geometric construction of the "Euclidean" momentum group manifold related to $\kappa$-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 behaviours for the spectral dimension according to the choice of deformed Laplacian, from dimensional reduction to super-diffusion.

12 pages, 8 figures; v2 short comments and references added

References in corpus (3)

• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Fractal properties of quantum spacetime
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime

Cited by in corpus (11)

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• Multifractional theories: an unconventional review
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• Multiscale spacetimes from first principles
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• Spectral dimensions and dimension spectra of quantum spacetimes
• UV dimensional reduction to two from group valued momenta
• Localization and diffusion in polymer quantum field theory
• Spectral Dimension of kappa-deformed space-time
• Entanglement entropy, scale-dependent dimensions and the origin of gravity