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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
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
Academic field: Physics
  • Mathematical Physics
Approach: Theoretical


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.

Published as SciPost Phys. Proc. 14, 024 (2023)

Author comments upon resubmission

Dear Editors,
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.

Submission & Refereeing History

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Resubmission scipost_202212_00026v2 on 21 April 2023

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