Multifractional theories: an updated review

Abstract

The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional paradigm to quantum gravity is discussed. We also clarify the issue of unitarity in theories with integer-order derivatives.

21 pages, 1 figure, 7 tables. Invited review article for the special issue "Fractional quantum theory" in Mod. Phys. Lett. A, ed. by S.C. Lim. v2: minor typos corrected, including in table 7 of the published version

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• Quantum mechanics in fractional and other anomalous spacetimes
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Cited by in corpus (23)

• Cosmology under the fractional calculus approach
• Revisiting Fractional Cosmology
• Exact solutions and cosmological constraints in fractional cosmology
• Ultraviolet-complete quantum field theories with fractional operators
• Estimated Age of the Universe in Fractional Cosmology
• Emergence of fractal cosmic space from fractional quantum gravity
• Gravitational potential and galaxy rotation curves in multi-fractional spacetimes
• Observational constraints on the fractal cosmology
• Path integral and conformal instability in nonlocal quantum gravity
• Black Hole Remnants from Dynamical Dimensional Reduction?
• Representations of the fractional d'Alembertian and initial conditions in fractional dynamics
• Newtonian Fractional-Dimension Gravity and the External Field Effect
• Newtonian Fractional-Dimension Gravity and Galaxies without Dark Matter
• Fractional Einstein field equations in $2+1$ dimensional spacetime
• Log-periodic gravitational-wave background beyond Einstein gravity
• Gravitational Foundations and Exact Solutions in $n$-Dimensional Fractional Cosmology
• Spacetime Foam Effects on Charged AdS Black Hole Thermodynamics
• Inflation and Primordial Perturbations in Fractal Cosmology
• On observational signatures of multi-fractional theory
• Diffusion method in field theories with fakeons
• Hawking area law in quantum gravity
• Cosmology of fractional gravity
• Relativistic Fractional-Dimension Gravity