2012/09/30 by Gianluca Calcagni, GIANLUCA CALCAGNI · 21 citations
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Asymptotic safety in quantum gravity #Cosmology and Gravitation Theories #Curse of dimensionality #Field (mathematics) #Fractal #Noncommutative and Quantum Gravity Theories #Quantum gravity #Renormalization group #Scale (ratio) #Spacetime #gr-qc #hep-th
paper · pdf · doi:10.1142/s0217751x13500929
published in International Journal of Modern Physics A 28(19), 1350092 (World Scientific) · 21 pages, 1 table. v2: discussion improved, references added
openalex publication_date 2013/07/24 · arxiv created 2013/07/30 · arxiv updated 2013/07/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We compare the recently formulated multifractional spacetimes with field theories of quantum gravity based on the renormalization group (RG), such as asymptotic safety and Hořava–Lifshitz gravity. The change of spacetime dimensionality with the probed scale is realized in both cases by an adaptation of the measurement tools ("rods") to the scale, but in different ways. In the multifractional case, by an adaptation of the position-space measure, which can be encoded into an explicit scale dependence of effective coordinates. In the case of RG-based theories, by an adaptation of the momenta. The two pictures are mapped into each other, thus presenting the fractal structure of spacetime in RG-based theories under an alternative perspective.