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 (24)

• Relativity in space-times with short-distance structure governed by an observer-independent (Planckian) length scale
• Spectral Dimension of the Universe in Quantum Gravity at a Lifshitz Point
• Bicrossproduct structure of $\kappa$-Poincare group and non-commutative geometry
• Spectral Dimension of the Universe
• The principle of relative locality
• Fractal Spacetime Structure in Asymptotically Safe Gravity
• Doubly Special Relativity theories as different bases of $\kappa$--Poincaré algebra
• Quantum field theory, gravity and cosmology in a fractal universe
• Fractal properties of quantum spacetime
• De Sitter space as an arena for Doubly Special Relativity
• Fractal Structure of Loop Quantum Gravity
• Doubly Special Relativity and de Sitter space
• Spectral geometry as a probe of quantum spacetime
• Born Reciprocity in String Theory and the Nature of Spacetime
• Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime
• Probing the quantum nature of spacetime by diffusion
• From dispersion relations to spectral dimension - and back again
• Fractional and noncommutative spacetimes
• Anomalous dimension in semiclassical gravity
• Living in Curved Momentum Space
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Black-hole entropy and minimal diffusion
• Unified description for kappa-deformations of orthogonal groups
• Representation Theory of Quantized Poincare Algebra. Tensor Operators and Their Application to One-Partical Systems

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• High temperature dimensional reduction in Snyder space
• Dimensional reduction in causal set gravity
• Planck-scale phenomenology with anti-de Sitter momentum space
• ABC of multi-fractal spacetimes and fractional sea turtles
• Spectral Dimension from Nonlocal Dynamics on Causal Sets
• Towards the map of quantum gravity
• Emergence of Spacetime in a restricted Spin-foam model
• Noncommutative fields and the short-scale structure of spacetime
• Spectral dimensions from the spectral action
• The Momentum Spaces of $\kappa$-Minkowski noncommutative spacetime
• Spontaneous Dimensional Reduction in Quantum Gravity
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• Signal propagation on $\kappa$-Minkowski spacetime and non-local two-point functions
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• Quantum gravity without vacuum dispersion
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• Vacuum energy and the cosmological constant problem in $\kappa$-Poincaré invariant field theories
• Hypothesis on the Nature of Time
• A group theoretic description of the $\kappa$-Poincaré Hopf algebra
• Vacuum energy from noncommutative models
• Dimensional flow in the kappa-deformed space-time
• Curvature effects in the spectral dimension of spin foams
• Reappraisal of a model for deformed special relativity
• Deformed phase spaces with group valued momenta
• Quantum gravity and gravitational-wave astronomy
• Finite entanglement entropy and spectral dimension in quantum gravity
• Ultralocal nature of geometrogenesis
• UV dimensional reduction to two from group valued momenta
• Non-Commutative space-time and Hausdorff dimension
• Thermal and spectral dimension of (generalized) Snyder noncommutative spacetimes
• From Causal Dynamical Triangulations To Astronomical Observations
• Localization and diffusion in polymer quantum field theory
• Spectral Dimension of kappa-deformed space-time
• Could LIV/noncommutativity alleviate the cosmological constant problem
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• The Weyl-Mellin quantization map for $\kappa$-Minkowski Noncommutative Spacetime
• Three-dimensional gravity and deformations of relativistic symmetries