Vertical extension of Noether theorem for scaling symmetries

Garcı́a, J. Antonio; Gutiérrez‐Ruiz, Daniel; Sánchez-Isidro, R. Abraham

doi:10.1140/epjp/s13360-020-00987-4

Cited by 5 publications

(2 citation statements)

References 17 publications

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“…We hope that the analysis initiated in this work will be helpful to clarify the origin and structure of scaling symmetries and their related invariants, by putting them on the same footing as other standard Noether symmetries. As further developments, we will address the comparison of our results with the 'Eisenhart-Duval lift' of mechanical systems employed in [41], with the 'vertical extension' of the tangent space presented in [19], with the reduction in the pre-symplectic setting described in [31], and also with the 'unit-free approach' to Hamiltonian mechanics introduced in [40], and we will provide a deeper analysis of the Lie-algebraic structure of the generalized Noether symmetries for various systems of interest in physics, e.g. in cosmology [33,34].…”

Section: Discussionmentioning

confidence: 97%

“…An interesting approach to solve some of the above puzzles has been presented in [19], where the authors construct a Noether theorem for scaling symmetries from the variational principle in the vertical extension of the standard phase space. The advantages of such approach are its general scope and the fact that it effectively yields invariants associated with scaling symmetries which do not depend on computing the on-shell action.…”

Section: Motivation and Previous Workmentioning

confidence: 99%

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A geometric approach to the generalized Noether theorem

Bravetti¹,

García-Chung²

2021

J. Phys. A: Math. Theor.

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We provide a geometric extension of the generalized Noether theorem for scaling symmetries recently presented by Zhang P-M et al (2020 Eur. Phys. J. Plus 135 223). Our version of the generalized Noether theorem has several positive features: it is constructed in the most natural extension of the phase space, allowing for the symmetries to be vector fields on such manifold and for the associated invariants to be first integrals of motion; it has a direct geometrical proof, paralleling the proof of the standard phase space version of Noether’s theorem; it automatically yields an inverse Noether theorem; it applies also to a large class of dissipative systems; and finally, it allows for a much larger class of symmetries than just scaling transformations which form a Lie algebra, and are thus amenable to algebraic treatments.

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Section: Discussionmentioning

confidence: 97%

Section: Motivation and Previous Workmentioning

confidence: 99%

A geometric approach to the generalized Noether theorem

Bravetti¹,

García-Chung²

2021

J. Phys. A: Math. Theor.

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Mechanical and radiation shielding features of lithium titanophosphate glasses doped BaO

Shaaban¹,

Al-Baradi²,

Alotaibi³

et al. 2023

Journal of Materials Research and Technology

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Addendum to: Dynamical torsion suppression in Brans–Dicke inflation and Lorentz violation (Eur Phys J C (2022)): Einstein–Cartan–Brans–Dicke–Maxwell universe with a chiral dynamo?

Andrade

2022

Eur. Phys. J. C

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We have recently shown that in Einstein–Cartan–Brans–Dicke (ECBD) gravity, torsion effects are not present in today’s universe because they are suppressed in a four-dimensional system, as in the bulk of five-dimensional braneworld endowed with torsion. In this addendum, we naturally introduce new features on the ECBD Maxwell Lagrangian dynamics deriving the chiral dynamo equation, and studying its physical properties. Magnetogenesis results are derived in this ECBDM universe. In particular we show, in the present universe, torsional magnetic fields of the second-order in the ohmic resistivity behave as $$B_{{\text {ECBD}}}=10^{-13}$$ B ECBD = 10 - 13 Gauss, which is exactly the estimate made by Miniati et al. (Phys Rev Lett, 2018) for the axion QCD magnetic field in the present universe. We found this at 1pc coherent length, whereas they found it at 20pc. To obtain this result, we consider a strong magnetic field of the order of the Biermann battery $$10^{30}G$$ 10 30 G . This seems to show that our model of ECBDM gravity can be used with success in inflationary magnetogenesis with torsion. Inflation or deflation are shown to depend upon torsion chirality. Torsion is shown to depend upon the BD parameter $${\omega }$$ ω and decays in time as in the reference to which this addendum refers (Garcia de Andrade in Eur Phys J C, 2002).

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Vertical extension of Noether theorem for scaling symmetries

Cited by 5 publications

References 17 publications

A geometric approach to the generalized Noether theorem

A geometric approach to the generalized Noether theorem

Mechanical and radiation shielding features of lithium titanophosphate glasses doped BaO

Addendum to: Dynamical torsion suppression in Brans–Dicke inflation and Lorentz violation (Eur Phys J C (2022)): Einstein–Cartan–Brans–Dicke–Maxwell universe with a chiral dynamo?

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