Fractional Analogous Models in Mechanics and Gravity Theories

Băleanu, Dumitru; Vacaru, Sergiu I.

doi:10.1007/978-1-4614-0457-6_16

Cited by 5 publications

(5 citation statements)

References 16 publications

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“…This proposal is much more rigorous than the previous one since it relies on the formalism of Finsler geometry [55] and, in particular, a structure of fractional manifold built with fractional differentials similar to those later employed in [14]. Once again, the Einstein equations were not derived from an action, although this should be possible using the fractional Euler-Lagrange equations found in [56,57]. A preliminary attempt to quantization was sketched in [58] but at a very formal level.…”

Section: Full Non-linear Theories Of Fractional Gravitymentioning

confidence: 99%

Classical and quantum gravity with fractional operators

Calcagni

2021

Class. Quantum Grav.

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Due to issues during the production process, a non-final version of the article was published without the author's approval. Classical and Quantum Gravity sincerely apologises for any inconvenience caused by this error, and confirms that the final results of the paper remain unaffected.The following errors are corrected in the article and missing elements are provided:(1) Page 1; a table of contents, missing from the original article, is included as follows:Contents

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Section: Full Non-linear Theories Of Fractional Gravitymentioning

confidence: 99%

Classical and quantum gravity with fractional operators

Calcagni

2021

Class. Quantum Grav.

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“…This proposal is much more rigorous than the previous one since it relies on the formalism of Finsler geometry [137] and, in particular, a structure of fractional manifold built with fractional differentials similar to those later employed in [42]. Once again, the Einstein equations were not derived from an action, although this should be possible using the fractional Euler-Lagrange equations found in [138,139]. A preliminary attempt to quantization was sketched in [140] but at a very formal level.…”

Section: Full Non-linear Theories Of Fractional Gravitymentioning

confidence: 99%

Quantum scalar field theories with fractional operators

Calcagni

2021

Preprint

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We study a class of perturbative scalar and gravitational quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension. These theories are either ghost free or power-counting renormalizable but they cannot be both at the same time. However, some of them are one-loop unitary and finite, and possibly unitary and finite at all orders. One of the theories is unitary and infrared-finite and can serve as a ghost-free model with large-scale modifications of general relativity. TheoryT [ + γ ] 4.2.1 Kinetic term and action 4.2.2 Dimensional flow 4.2.3 Unitarity, renormalization and range of γ 4.3 Theory T [ γ(ℓ) ] 4.3.1 Kinetic term and action 4.3.2 Dimensional flow 4.3.3 Unitarity, renormalization and range of γ 5 Gravity 5.1 Gravity with fractional derivatives 5.1.1 Theory T [∂ γ ] 5.1.2 Theory T [∂ + ∂ γ ] 5.1.3 Theory T [∂ γ(ℓ) ] 5.2 Gravity with fractional d'Alembertian 5.2.1 Theory T [ γ ] 5.2.2 Theory T [ + γ ] 5.2.3 Theory T [ γ(ℓ) ] 6 Comparison with the literature 6.1 Scalar field 6.2 Gravity 6.2.1 Limited portions of fractional gravity 6.2.2 Full non-linear theories of fractional gravity 6.2.3 Other theories of quantum or non-local gravity 7 Conclusions and perspective A Properties of fractional derivatives B Alternative proof of unitarity C Equations of motion in fractional gravity C.1 Derivation of (5.17) C.2 Derivation of (5.21) and (5.33

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Section: Full Non-linear Theories Of Fractional Gravitymentioning

confidence: 99%

Classical and quantum gravity with fractional operators

Calcagni

2021

Preprint

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Following the same steps made for a scalar field in a parallel publication, we propose a class of perturbative theories of quantum gravity based on fractional operators, where the kinetic operator of the graviton is either made of fractional derivatives or a covariant fractional d'Alembertian. The classical action for each theory is constructed and the equations of motion are derived. Unitarity and renormalizability of theories with a fractional d'Alembertian are also considered. We argue that unitarity and power-counting renormalizability never coexist, although in some cases one-loop unitary and finiteness are possible. One of the theories is unitary and infrared-finite and can serve as a ghost-free model with large-scale modifications of general relativity.

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Fractional Analogous Models in Mechanics and Gravity Theories

Abstract: We briefly review our recent results on the geometry of nonholonomic manifolds and Lagrange-Finsler spaces and fractional calculus with Caputo derivatives. Such constructions are used for elaborating analogous models of fractional gravity and fractional Lagrange mechanics.

Cited by 5 publications

References 16 publications

Classical and quantum gravity with fractional operators

Classical and quantum gravity with fractional operators

Quantum scalar field theories with fractional operators

Classical and quantum gravity with fractional operators

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