2009/01/13 by Saurya Das, Elias C. Vagenas · 2 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Applications #gr-qc #hep-ph #hep-th #quant-ph
paper · pdf · doi:10.1139/p08-105
published as Can.J.Phys.87:233-240,2009 · 7 pages. Based on talk by S. Das at Theory Canada 4, Montreal, 4 June, 2008. To be published in the Canadian Journal of Physics
arxiv created 2009/01/13 · crossref issued 2009/03/01 · crossref published 2009/03/01 · crossref published-print 2009/03/01 · openalex publication_date 2009/03/01 · crossref created 2009/07/08 · arxiv updated 2010/11/02 · openalex created_date 2022/09/15 · crossref deposited 2025/07/02 · crossref indexed 2026/07/29 · openalex updated_date 2026/07/30
Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms in any quantum mechanical Hamiltonian, proportional to βp4 and β2 p6 respectively, where β∼ 1/(MPlc)2 is the GUP parameter. These terms become important at or above the Planck energy. Considering only the first of these, and treating it as a perturbation, we show that the GUP affects the Lamb shift, Landau levels, reflection and transmission coefficients of a potential step and potential barrier, and the current in a Scanning Tunnel Microscope (STM). Although these are too small to be measurable at present, we speculate on the possibility of extracting measurable predictions in the future.