Introduction to multifractional spacetimes

Journal Article · Mon Sep 24 00:00:00 EDT 2012 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4756961· OSTI ID:22075573

Calcagni, Gianluca ^[1]

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1. Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muehlenberg 1, D-14476 Golm, Germany and Instituto de Estructura de la Materia, IEM-CSIC, Serrano 121, 28006 Madrid (Spain)

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 Poincare 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.

• OSTI ID: 22075573
• Journal Information: AIP Conference Proceedings, Vol. 1483, Issue 1; Conference: 6. international school on field theory and gravitation 2012, Petropolis, RJ (Brazil), 23-27 Apr 2012; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FRACTALS
GEOMETRY
GRAVITATION
INFRARED DIVERGENCES
QUANTUM GRAVITY
RENORMALIZATION
SPACE-TIME
SYMMETRY
ULTRAVIOLET RADIATION