https://doi.org/10.1140/epjc/s10052-023-11480-4
Regular Article - Theoretical Physics
Extended GUP formulation and the role of momentum cut-off
1
Physics Department, ‘Sapienza’ University of Rome, P.le Aldo Moro 5, 00185, Rome, Italy
2
ENEA, FSN-FUSPHY-TSM R.C. Frascati, Via E. Fermi 45, 00044, Frascati, Italy
a
sebastiano.segreto@uniroma1.it
Received:
4
October
2022
Accepted:
6
April
2023
Published online:
10
May
2023
We analyze the extension of the GUP theory deriving from the modified uncertainty principle in agreement with the string low energy limit, which represents one of the most general formulations satisfying the Jacobi identity, in the context of the associative algebras. After providing some physical insights on the nature of the considered approaches exploiting the cosmological arena, first, we show how a natural formulation of the theory in an infinite momentum space does not lead to the emergence of a nonzero minimal uncertainty in position, then we construct a truncated formulation of the theory in momentum space, proving that only in this case we can recover the desired feature of the presence of a nonzero minimal uncertainty in position, which – as usual in these theories – can be interpreted as a phenomenological manifestation of cut-off physics effects. Both quantization schemes are completely characterized and finally applied to study wave packets’ behavior and their evolution in time. The obtained results can shed light on which generalizations of the GUP theory are more coherent with the string low energy limit, in view of the existence of a minimum length in the form of a minimal uncertainty in position.
© The Author(s) 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.
