Introduction to multifractional spacetimes
High Energy Physics - Theory
2012-10-10 v2 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
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 Poincar\'e 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.
Cite
@article{arxiv.1209.1110,
title = {Introduction to multifractional spacetimes},
author = {Gianluca Calcagni},
journal= {arXiv preprint arXiv:1209.1110},
year = {2012}
}
Comments
26 pages, 6 figures; v2: references added. Lectures given at Sixth International School on Field Theory and Gravitation 2012 (Petropolis, Brazil)