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.

arXiv comment21 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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• 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
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• Fractional Einstein field equations in $2+1$ dimensional spacetime
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• Diffusion method in field theories with fakeons
• Hawking area law in quantum gravity
• Cosmology of fractional gravity
• Relativistic Fractional-Dimension Gravity