{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T11:05:52Z","timestamp":1777633552660,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,12,4]],"date-time":"2019-12-04T00:00:00Z","timestamp":1575417600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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   \u2212 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 \u00d7  10  \u2212 19    m     and are in full agreement with previous studies on black holes.<\/jats:p>","DOI":"10.3390\/sym11121478","type":"journal-article","created":{"date-parts":[[2019,12,5]],"date-time":"2019-12-05T03:16:36Z","timestamp":1575515796000},"page":"1478","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Constraints on the String T-Duality Propagator from the Hydrogen Atom"],"prefix":"10.3390","volume":"11","author":[{"given":"Michael F.","family":"Wondrak","sequence":"first","affiliation":[{"name":"Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Stra\u00dfe 1, 60438 Frankfurt am Main, Germany"},{"name":"Institut f\u00fcr Theoretische Physik, Johann Wolfgang Goethe-Universit\u00e4t Frankfurt am Main, Max-von-Laue-Stra\u00dfe 1, 60438 Frankfurt am Main, Germany"}]},{"given":"Marcus","family":"Bleicher","sequence":"additional","affiliation":[{"name":"Frankfurt Institute for Advanced Studies (FIAS), Ruth-Moufang-Stra\u00dfe 1, 60438 Frankfurt am Main, Germany"},{"name":"Institut f\u00fcr Theoretische Physik, Johann Wolfgang Goethe-Universit\u00e4t Frankfurt am Main, Max-von-Laue-Stra\u00dfe 1, 60438 Frankfurt am Main, Germany"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,4]]},"reference":[{"key":"ref_1","unstructured":"Weinberg, S. 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