Fractional Derivative Regularization in QFT

Tarasov, Vasily E.

doi:10.48550/arxiv.1805.08566

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2020

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“…Fractional calculus [26][27][28] offers a reliable set of tools for describing several physical phenomena which are not typically accounted for by model based on ordinary calculus (see e.g., [28][29][30]). In recent years, this mathematical scheme has also been applied, in various forms, to gravity and fundamental physics, see e.g., [31][32][33][34]. Focusing on the problem of dark matter phenomenology, the first fractional MOND-like non-relativistic potential theory was proposed by A. Giusti in [35].…”

Section: Introductionmentioning

confidence: 99%

On the Kuzmin model in fractional Newtonian gravity

Giusti,

Garrappa,

Vachon

2020

Preprint

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Fractional Newtonian gravity, based on the fractional generalization of Poisson's equation for Newtonian gravity, is a novel approach to Galactic dynamics aimed at providing an alternative to the dark matter paradigm through a non-local modification of Newton's theory. We provide an in-depth discussion of the gravitational potential for the Kuzmin disk within this new approach. Specifically, we derive an integral and a series representation for the potential, we verify its asymptotic behavior at large scales, and we provide illuminating plots of the resulting equipotential surfaces.

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