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Open AccessArticle

Constraints on the String T-Duality Propagator from the Hydrogen Atom

1
Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Straße 1, 60438 Frankfurt am Main, Germany
2
Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität Frankfurt am Main, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(12), 1478; https://doi.org/10.3390/sym11121478
Received: 17 October 2019 / Revised: 27 November 2019 / Accepted: 29 November 2019 / Published: 4 December 2019
(This article belongs to the Special Issue Modified Theories of Gravity)
We investigated the implications of string theory in the high-precision regime of quantum mechanics. In particular, we examined a quantum field theoretical propagator which was derived from string theory when compactified at the T-duality self-dual radius and which is closely related to the path integral duality. Our focus was on the hydrogen ground state energy and the 1 S 1 / 2 2 S 1 / 2 transition frequency, as they are the most precisely explored properties of the hydrogen atom. The T-duality propagator alters the photon field dynamics leading to a modified Coulomb potential. Thus, our study is complementary to investigations where the electron evolution is modified, as in studies of a minimal length in the context of the generalized uncertainty principle. The first manifestation of the T-duality propagator arises at fourth order in the fine-structure constant, including a logarithmic term. For the first time, constraints on the underlying parameter, the zero-point length, are presented. They reach down to 3.9 × 10 19 m and are in full agreement with previous studies on black holes. View Full-Text
Keywords: string T-duality; zero-point length; minimal length; extra dimensions; modified Coulomb potential; hydrogen energy levels string T-duality; zero-point length; minimal length; extra dimensions; modified Coulomb potential; hydrogen energy levels
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Wondrak, M.F.; Bleicher, M. Constraints on the String T-Duality Propagator from the Hydrogen Atom. Symmetry 2019, 11, 1478.

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