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Fractional and noncommutative spacetimes

MPS-Authors
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Calcagni,  Gianluca
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Oriti,  D.
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

Scalisi,  Marco
Microscopic Quantum Structure & Dynamics of Spacetime, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1107.5308
(Preprint), 337KB

PRD84_125002.pdf
(Any fulltext), 251KB

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Citation

Arzano, M., Calcagni, G., Oriti, D., & Scalisi, M. (2011). Fractional and noncommutative spacetimes. Physical Review D, 84(12): 125002. doi:10.1103/PhysRevD.84.125002.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0012-313B-2
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 \kappa-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 \kappa-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.