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Journal Article

#### Fractional and noncommutative spacetimes

##### Locator

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##### Fulltext (public)

1107.5308

(Preprint), 337KB

PRD84_125002.pdf

(Any fulltext), 251KB

##### Supplementary Material (public)

There is no public supplementary material available

##### 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.