Fractional and noncommutative spacetimes

Michele Arzano, Gianluca Calcagni, Daniele Oriti, and Marco Scalisi
Phys. Rev. D 84, 125002 – Published 2 December 2011

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 nonrotation-invariant but cyclicity-preserving measure of κ-Minkowski spacetime. 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.

  • Received 26 July 2011

DOI:https://doi.org/10.1103/PhysRevD.84.125002

© 2011 American Physical Society

Authors & Affiliations

Michele Arzano1,*, Gianluca Calcagni2,†, Daniele Oriti2,‡, and Marco Scalisi2,3,4,§

  • 1Institute for Theoretical Physics and Spinoza Institute, Utrecht University, Leuvenlaan 4, Utrecht 3584 TD, The Netherlands
  • 2Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Golm, Germany
  • 3Dipartimento di Fisica e Astronomia, Università di Catania
  • 4INFN Sezione di Catania, Via Santa Sofia 64, I-95023 Catania, Italy

  • *m.arzano@uu.nl
  • calcagni@aei.mpg.de
  • doriti@aei.mpg.de
  • §marco.scalisi@aei.mpg.de

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Vol. 84, Iss. 12 — 15 December 2011

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