Hilbert space representation of maximal length and minimal momentum uncertainties

• URL: http://arxiv.org/abs/2110.09926v1
• Date: Mon, 18 Oct 2021 15:11:54 GMT
• Title: Hilbert space representation of maximal length and minimal momentum uncertainties
• Authors: Kossi Amouzouvi, Benjamin A. Appiah, Lat\'evi M. Lawson and Abdel-Baset A. Mohamed
• Abstract summary: We show that the maximal length scale naturally emerges in the context of cosmological particle's horizon or cosmic topology. We derive the maximal length uncertainty and its corresponding minimal momentum from the generalized uncertainty principle. We also construct the corresponding Fourier transform and its inverse representations.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Perivolaropoulos has recently proposed a position-deformed Heisenberg algebra which includes a maximal length [Phys.Rev.95, 103523 (2017)]. He has shown that this length scale naturally emerges in the context of cosmological particle's horizon or cosmic topology. Following this work, we propose a new deformed algebra and derive the maximal length uncertainty and its corresponding minimal momentum uncertainty from the generalized uncertainty principle. We also construct the corresponding Fourier transform and its inverse representations. Finally, we propose n-dimensional representation of this algebra

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