Introduction to multifractional spacetimes
arXiv:1209.1110 · doi:10.1063/1.4756961
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.
26 pages, 6 figures; v2: references added. Lectures given at Sixth International School on Field Theory and Gravitation 2012 (Petropolis, Brazil)
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- Metric dimensional reduction at singularities with implications to Quantum Gravity
- Symmetries and propagator in multifractional scalar field theory
- Standard Model in multiscale theories and observational constraints
- Particle-physics constraints on multifractal spacetimes
- Spontaneous Spacetime Reduction and Unitary Weak Boson Scattering at the LHC
- Reduction of gravity-matter and dS gravity to hypersurface
- 4D covariance of holographic quantization of Einstein gravity
- Spectral dimension in graph models of causal quantum gravity