Phenomenological implications of the generalized uncertainty principle
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Date
2016-01-18
Authors
Das, Saurya
Vagenas, Elias C.
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Abstract
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 p4 and 2p6 respectively, where 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.
Description
Sherpa Romeo green journal. Permission to archive author manuscript.
Keywords
Generalized uncertainty principle , GUP , Lamb shift , Landau levels
Citation
Das, S., & Vagenas, E. C. (2009). Phenomenological implications of the generalized uncertainty principle. Canadian Journal of Physics, 2009, 87(3), 233-240. https://doi.org/10.1139/P08-105