On the Minimal Length Uncertainty Relation and the Foundations of String Theory

Abstract

We review our work on the minimal length uncertainty relation as suggested by perturbative string theory. We discuss simple phenomenological implications of the minimal length uncertainty relation and then argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the implication of this for the problem of vacuum energy and the foundations of non-perturbative string theory.

Inner horizon of the quantum Reissner-Nordström black holes

“…one very narrow Gaussian wave-function), the uncertainty in the location of the outer horizon ∆R + grows with the mass of the source (since ∼ m −1 ). This is in agreement with many postulated GUPs in the presence of gravity [21,22], but implies that when the source is of astrophysical Open Access. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.…”

Ground state of the hydrogen atom via Dirac equation in a minimal-length scenario

“…(5), (6) and (7). In order to avoid the problem of substitutingX i for derivatives ofp i in the Coulomb potential ( 1 r ) we have used the "position" representation given by equations (8) and (9). With the introduction of the Coulomb potential in the new Dirac energy operator obtained by replacement ofp i byP i in the ordinary Dirac Hamiltonian, we have found a expression for the energy shift of the hydrogen atom via perturbation theory, since we have assumed that the electron mass is much smaller than the mass scale of the minimal length (see Eq.…”

“…Over the years, many works have been published about minimal length in different contexts. For more about ideas of the existence of a minimal length and its implementation, the interested reader is referred to references [8,9,10,11].…”

A Scale at 10 MeV, Gravitational Topological Vacuum, and Large Extra Dimensions

“…In the effort to understand the smallness of the cosmological constant, several numerical relations among the energy scales have been noticed (or proposed) in the literature that mimic a see-saw-type suppression mechanism [67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82].…”