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Newton mechanics, Galilean relativity, and special relativity in $\alpha$-deformed binary operation setting
by Won S. Chung and Mahouton N. Hounkonnou
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Submission summary
| Authors (as registered SciPost users): | Mahouton Norbert Hounkonnou |
| Submission information | |
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| Preprint Link: | scipost_202212_00026v1 (pdf) |
| Date submitted: | 2022-12-14 16:25 |
| Submitted by: | Hounkonnou, Mahouton Norbert |
| Submitted to: | SciPost Physics Proceedings |
| Proceedings issue: | 34th International Colloquium on Group Theoretical Methods in Physics (GROUP2022) |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We define new velocity and acceleration having dimension of $(Length)^{\alpha}/(Time)$ and $(Length)^{\alpha}/(Time)^2,$ respectively, based on the fractional addition rule. We discuss the formulation of fractional Newton mechanics, Galilean relativity and special relativity in the same setting. We show the conservation of the fractional energy, characterize the Lorentz transformation and group, and derive the expressions of the energy and momentum. The two body decay is discussed as a concrete illustration.
Current status:
Has been resubmitted
Anonymous on 2023-04-17 [id 3593]
In this paper the authors present parallel versions of classical Newtonian mechanics and Einstein restricted relativity using pseudo-analysis instead of conventional analysis by introducing an $\alpha$-deformation of the usual binary operations in the field of real numbers. Thus they consider a ``deformation'' $|x|^{\alpha -1}\,x$ instead of $x$, thereby obtaining a new definition of the derivative. In this way they develop an $\alpha$-deformation of Newtonian mechanics as well as Einstein relativity.
The article is interesting because it explores new models of theories close to the physics with $\alpha =1$ that we know so far.
The authors present some small notions about the Galilei and Lorentz groups, but at no point do they comment at least qualitatively on their corresponding Lie algebras, which they should do in the definitive version.
In the introduction there is a sentence in which it is said that Einstein used the pseudo-analysis for the velocity addition formula. I think it would be more convenient to say that the velocity addition formula can be recovered by using the pseudo-analysis.
Completing these requirements I recommend the publication of the paper.