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arXiv · 1107.5308

Fractional and noncommutative spacetimes

Michele Arzano·Gianluca Calcagni·Daniele Oriti·Marco Scalisi
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Abstract

We establish a mapping between fractional and noncommutative spacetimes in configuration space. Depending on the scale at which the relation is considered, there arise two possibilities. For a fractional spacetime with log-oscillatory measure, the effective measure near the fundamental scale determining the log-period coincides with the non-rotation-invariant but cyclicity-preserving measure of κ-Minkowski. At scales larger than the log-period, the fractional measure is averaged and becomes a power-law with real exponent. This can be also regarded as the cyclicity-inducing measure in a noncommutative spacetime defined by a certain nonlinear algebra of the coordinates, which interpolates between κ-Minkowski and canonical spacetime. These results are based upon a braiding formula valid for any nonlinear algebra which can be mapped onto the Heisenberg algebra.

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Michele Arzano, Gianluca Calcagni, Daniele Oriti, Marco Scalisi. 2011-12-02. Fractional and noncommutative spacetimes. https://doi.org/10.1103/physrevd.84.125002

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