Introduction to multifractional spacetimes

Gianluca Calcagni

doi:10.1063/1.4756961

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arXiv · 1209.1110

Introduction to multifractional spacetimes

Gianluca Calcagni

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Abstract

We informally review the construction of spacetime geometries with multifractal and, more generally, multiscale properties. Based on fractional calculus, these continuous spacetimes have their dimension changing with the scale; they display discrete symmetries in the ultraviolet and ordinary Poincaré symmetries in the infrared. Under certain reasonable assumptions, field theories (including gravity) on multifractional geometries are generally argued to be perturbatively renormalizable. We also sketch the relation with other field theories of quantum gravity based on the renormalization group.

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Gianluca Calcagni. 2012-10-09. Introduction to multifractional spacetimes. https://doi.org/10.1063/1.4756961

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