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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
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Mahouton Norbert Hounkonnou |
| Submission information | |
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| Preprint Link: | scipost_202212_00026v2 (pdf) |
| Date accepted: | 2023-07-21 |
| Date submitted: | 2023-04-21 19:47 |
| 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.
Author comments upon resubmission
Please find enclosed the revised version of our paper.
Sincerely yours,
M. N. Hounkonnou
(On behalf of all authors)
List of changes
Reply to the referee
We thank the referee for his useful comments.
1. A comment is made, in the Conclusion, on the important questions concerning the Galilei and Lorentz groups, and their corresponding Lie algebras.
2. We have reformulated the sentence, in the Introduction, on the use of the pseudo-analysis for the velocity addition formula by Einstein.
Published as SciPost Phys. Proc. 14, 024 (2023)